An order-16 bordered diagonal magic cube [Mitsutoshi Nakamura, July 2004]
   This magic cube is a bordered diagonal magic cube that I constructed at first in the world.
   The magic cube is itself diagonal, that is, every (horizontal or vertical) diagonal of the cube is magic. Of course, every triagonal is magic, too.
Furthermore, it contains sub magic cubes of orders 4, 6, 8, 10, 12, and 14 which satisfy the following properties:
   The order-4 sub cube is a magic cube which consists of consecutive integers and every horizontal diagonal is magic.
Of course, every triagonal of the sub cube is magic, too.
Each of the sub cubes of orders 6, 8, 10, 12, and 14 is a diagonal magic cube which consists of consecutive integers. 
Consequently, every (horizontal or vertical) diagonal of the sub cube is magic. Of course, every triagonal of the sub cube is magic, too.
(It is impossible to make the order-4 sub cube a diagonal magic cube.)
   Each of these sub cubes can transform to a normal magic cube by subtracting some constant dependent on the order of the sub cube 
from each of the cells of the sub cube.
Particularly, every sub cube whose order is 6 or higher becomes a normal bordered diagonal magic cube again by the tranformation.
   Furthermore, this magic cube contains a lot of magic squares. 
For example, each of the Planes No. 1 and No. 16 inlays an order-12 magic square which contains 6 order-8 magic squares and 15 order-4 magic sqaures,
and each of the Planes Nos. 2, 3, 14, and 15 inlays an order-8 magic square which contains 6 order-4 magic squares.
Vertical slices of the cube contain similar magic squares, too.
   The Planes from No. 7 to No. 10 are non-normal concentric magic squares.
Plane No. 1
49 39 91 75 4025 4007 105 3989 3980 120 177 3917 3908 192 4055 4047 32776
36 4050 4003 4005 80 76 103 3987 3982 122 175 3915 3910 194 48 4090 32776
88 4077 245 3840 3850 259 261 3824 3834 275 277 3808 3818 291 13 4016 32776
82 3999 260 3849 3839 246 276 3833 3823 262 292 3817 3807 278 4092 21 32776
4014 96 3847 254 252 3841 3831 270 268 3825 3815 286 284 3809 9 4075 32776
4011 4072 3842 251 253 3848 3826 267 269 3832 3810 283 285 3816 32 79 32776
153 3945 293 3792 3802 307 309 3776 3786 323 325 3760 3770 339 3947 149 32776
3941 157 308 3801 3791 294 324 3785 3775 310 340 3769 3759 326 159 3937 32776
3932 164 3799 302 300 3793 3783 318 316 3777 3767 334 332 3761 162 3936 32776
168 3928 3794 299 301 3800 3778 315 317 3784 3762 331 333 3768 3926 172 32776
225 3873 341 3744 3754 355 357 3728 3738 371 373 3712 3722 387 3875 221 32776
3869 229 356 3753 3743 342 372 3737 3727 358 388 3721 3711 374 231 3865 32776
3860 236 3751 350 348 3745 3735 366 364 3729 3719 382 380 3713 234 3864 32776
240 3856 3746 347 349 3752 3730 363 365 3736 3714 379 381 3720 3854 244 32776
4062 53 4030 28 4079 85 3990 106 119 3979 3918 178 191 3907 4043 8 32776
4046 2 70 4086 10 4026 3996 112 113 3973 3924 184 185 3901 4096 52 32776
32776 32776 32776 32776 32776 32776 32776 32776 32776 32776 32776 32776 32776 32776 32776 32776 32776 32776
Plane No. 2
6 4042 4064 4028 68 4082 3993 109 116 3976 3921 181 188 3904 58 40 32776
4054 683 696 705 3335 763 782 3314 3215 883 902 3194 3390 3404 3413 43 32776
4023 744 3417 706 754 3326 3323 791 874 3206 3203 911 3396 679 3349 74 32776
4020 737 3398 3388 3340 768 777 3309 3220 888 897 3189 711 702 3355 77 32776
84 3255 841 839 993 3092 3102 1007 1009 3076 3086 1023 3261 3262 833 4013 32776
87 843 3253 3251 1008 3101 3091 994 1024 3085 3075 1010 849 850 3245 4010 32776
151 862 3236 3238 3099 1002 1000 3093 3083 1018 1016 3077 856 855 3244 3946 32776
3939 3234 864 866 3094 999 1001 3100 3078 1015 1017 3084 3228 3227 872 158 32776
3934 3135 961 959 1025 3060 3070 1039 1041 3044 3054 1055 3141 3142 953 163 32776
170 963 3133 3131 1040 3069 3059 1026 1056 3053 3043 1042 969 970 3125 3927 32776
223 982 3116 3118 3067 1034 1032 3061 3051 1050 1048 3045 976 975 3124 3874 32776
3867 3114 984 986 3062 1031 1033 3068 3046 1047 1049 3052 3108 3107 992 230 32776
3862 3356 3393 3389 758 3330 3319 787 878 3210 3199 907 712 698 743 235 32776
242 3359 687 3400 760 3332 3317 785 880 3212 3197 905 695 3405 745 3855 32776
57 3412 700 703 3344 772 773 3305 3224 892 893 3185 3387 3403 686 4040 32776
4057 55 33 69 4029 15 104 3988 3981 121 176 3916 3909 193 4039 4091 32776
32776 32776 32776 32776 32776 32776 32776 32776 32776 32776 32776 32776 32776 32776 32776 32776 32776 32776
Plane No. 3
61 4035 389 404 3703 3698 437 452 3655 3650 485 500 3607 3602 4034 64 32776
4073 714 3416 3378 761 3333 3316 784 881 3213 3196 904 3376 691 716 24 32776
533 3419 1233 1223 1275 1259 2841 2823 1289 2805 2796 1304 2871 2863 678 3564 32776
3552 739 1220 2866 2819 2821 1264 1260 1287 2803 2798 1306 1232 2906 3358 545 32776
3562 834 1272 2893 1357 2728 2738 1371 1373 2712 2722 1387 1197 2832 3263 535 32776
547 3246 1266 2815 1372 2737 2727 1358 1388 2721 2711 1374 2908 1205 851 3550 32776
549 3243 2830 1280 2735 1366 1364 2729 2719 1382 1380 2713 1193 2891 854 3548 32776
3536 871 2827 2888 2730 1363 1365 2736 2714 1379 1381 2720 1216 1263 3226 561 32776
3546 954 1337 2761 1389 2696 2706 1403 1405 2680 2690 1419 2763 1333 3143 551 32776
563 3126 2757 1341 1404 2705 2695 1390 1420 2689 2679 1406 1343 2753 971 3534 32776
565 3123 2748 1348 2703 1398 1396 2697 2687 1414 1412 2681 1346 2752 974 3532 32776
3520 991 1352 2744 2698 1395 1397 2704 2682 1411 1413 2688 2742 1356 3106 577 32776
3530 3361 2878 1237 2846 1212 2895 1269 2806 1290 1303 2795 2859 1192 736 567 32776
579 677 2862 1186 1254 2902 1194 2842 2812 1296 1297 2789 2912 1236 3420 3518 32776
27 3381 681 719 3336 764 781 3313 3216 884 901 3193 721 3406 3383 4070 32776
4033 62 3708 3693 394 399 3660 3645 442 447 3612 3597 490 495 63 4036 32776
32776 32776 32776 32776 32776 32776 32776 32776 32776 32776 32776 32776 32776 32776 32776 32776 32776 32776
Plane No. 4
3997 73 3696 3705 398 395 3648 3657 446 443 3600 3609 494 491 4094 30 32776
93 729 720 3374 759 3331 3318 786 879 3211 3198 906 3369 3367 732 4004 32776
548 3346 1190 2858 2880 2844 1252 2898 2809 1293 1300 2792 1242 1224 751 3549 32776
3561 3364 2870 1555 1568 1577 2463 1635 1654 2442 2518 2532 2541 1227 733 536 32776
3551 3260 2839 1616 2545 1578 1626 2454 2451 1663 2524 1551 2477 1258 837 546 32776
534 848 2836 1609 2526 2516 2468 1640 1649 2437 1583 1574 2483 1261 3249 3563 32776
564 857 1268 2383 1713 1711 1745 2340 2350 1759 2389 2390 1705 2829 3240 3533 32776
3545 3229 1271 1715 2381 2379 1760 2349 2339 1746 1721 1722 2373 2826 868 552 32776
3535 3140 1335 1734 2364 2366 2347 1754 1752 2341 1728 1727 2372 2762 957 562 32776
550 968 2755 2362 1736 1738 2342 1751 1753 2348 2356 2355 1744 1342 3129 3547 32776
580 977 2750 2484 2521 2517 1630 2458 2447 1659 1584 1570 1615 1347 3120 3517 32776
3529 3109 1354 2487 1559 2528 1632 2460 2445 1657 1567 2533 1617 2743 988 568 32776
3519 740 1241 2540 1572 1575 2472 1644 1645 2433 2515 2531 1558 2856 3357 578 32776
566 747 2873 1239 1217 1253 2845 1199 1288 2804 2797 1305 2855 2907 3350 3531 32776
37 3365 3377 723 3338 766 779 3311 3218 886 899 3191 728 730 3368 4060 32776
4067 4024 401 392 3699 3702 449 440 3651 3654 497 488 3603 3606 3 100 32776
32776 32776 32776 32776 32776 32776 32776 32776 32776 32776 32776 32776 32776 32776 32776 32776 32776 32776
Plane No. 5
99 4000 3706 3695 396 397 3658 3647 444 445 3610 3599 492 493 29 4066 32776
4008 3295 794 3300 1057 1072 3035 3030 1089 1104 3003 2998 798 800 3304 89 32776
3559 801 1245 2851 1421 1436 2671 2666 1453 1468 2639 2634 2850 1248 3296 538 32776
542 799 2889 1586 2544 2506 1633 2461 2444 1656 2504 1563 1588 1208 3298 3555 32776
540 1121 1485 2547 1841 1831 1883 1867 2233 2215 2263 2255 1550 2612 2976 3557 32776
3553 2964 2600 1611 1828 2258 2211 2213 1872 1868 1840 2298 2486 1497 1133 544 32776
3543 2974 2610 1706 1880 2285 1893 2192 2202 1907 1805 2224 2391 1487 1123 554 32776
558 1135 1499 2374 1874 2207 1908 2201 2191 1894 2300 1813 1723 2598 2962 3539 32776
556 1137 1501 2371 2222 1888 2199 1902 1900 2193 1801 2283 1726 2596 2960 3541 32776
3537 2948 2584 1743 2219 2280 2194 1899 1901 2200 1824 1871 2354 1513 1149 560 32776
3527 2958 2594 2489 2270 1845 2238 1820 2287 1877 2251 1800 1608 1503 1139 570 32776
574 1151 1515 1549 2254 1794 1862 2294 1802 2234 2304 1844 2548 2582 2946 3523 32776
572 3301 1211 2509 1553 1591 2464 1636 1653 2441 1593 2534 2511 2886 796 3525 32776
3521 3302 2849 1246 2676 2661 1426 1431 2644 2629 1458 1463 1247 2852 795 576 32776
4056 793 3303 797 3040 3025 1062 1067 3008 2993 1094 1099 3299 3297 802 41 32776
31 97 391 402 3701 3700 439 450 3653 3652 487 498 3605 3604 4068 3998 32776
32776 32776 32776 32776 32776 32776 32776 32776 32776 32776 32776 32776 32776 32776 32776 32776 32776 32776
Plane No. 6
4038 60 403 390 3697 3704 451 438 3649 3656 499 486 3601 3608 65 4031 32776
4071 803 3286 808 3028 3037 1066 1063 2996 3005 1098 1095 3290 3292 812 26 32776
3554 3293 2813 1257 2664 2673 1430 1427 2632 2641 1462 1459 2910 1214 804 543 32776
539 3291 1277 1601 1592 2502 1631 2459 2446 1658 2497 2495 1604 2820 806 3558 32776
541 1136 1500 2474 1798 2250 2272 2236 1860 2290 1850 1832 1623 2597 2961 3556 32776
3560 2973 2609 2492 2262 1947 1988 2098 1998 2111 2149 1835 1605 1488 1124 537 32776
3538 2963 2599 2388 2231 1983 2156 2009 2087 1942 2114 1866 1709 1498 1134 559 32776
555 1122 1486 1720 2228 2121 2082 2004 2014 2094 1976 1869 2377 2611 2975 3542 32776
557 1152 1516 1729 1876 1955 2013 2095 2081 2005 2142 2221 2368 2581 2945 3540 32776
3544 2957 2593 2357 1879 2137 1943 2086 2012 2153 1960 2218 1740 1504 1140 553 32776
3522 2947 2583 1612 1849 2148 2109 1999 2099 1986 1950 2248 2485 1514 1150 575 32776
571 1138 1502 1619 2265 1847 1825 1861 2237 1807 2247 2299 2478 2595 2959 3526 32776
573 809 1221 2493 2505 1595 2466 1638 1651 2439 1600 1602 2496 2876 3288 3524 32776
3528 810 2883 2840 1433 1424 2667 2670 1465 1456 2635 2638 1187 1284 3287 569 32776
19 3285 811 3289 1069 1060 3031 3034 1101 1092 2999 3002 807 805 3294 4078 32776
66 4037 3694 3707 400 393 3646 3659 448 441 3598 3611 496 489 4032 59 32776
32776 32776 32776 32776 32776 32776 32776 32776 32776 32776 32776 32776 32776 32776 32776 32776 32776 32776
Plane No. 7
129 127 405 420 3687 3682 453 468 3639 3634 501 516 3591 3586 3966 3972 32776
3969 822 3283 817 3038 3027 1064 1065 3006 2995 1096 1097 3279 3277 813 128 32776
581 3276 1283 2816 2674 2663 1428 1429 2642 2631 1460 1461 1213 2882 821 3516 32776
3504 3278 2824 2423 1666 2428 1761 1776 2331 2326 1670 1672 2432 1273 819 593 32776
3514 2971 2607 1673 1853 2243 1909 1924 2183 2178 2242 1856 2424 1490 1126 583 32776
595 1130 1494 1671 2281 1975 2152 1978 2105 1951 2130 1816 2426 2603 2967 3502 32776