### 5x5x5 magic cube

See on www.trump.de/magic-squares/magic-cubes/cubes-1.html the following (semi pan)magic 5x5x5 cube.

 The first known perfect magic cube of order 5 Walter Trump and Christian Boyer, 2003-11-13

This 5x5x5 magic cube has as magic features:

• the 5 rows, the 5 columns and the 2 diagonals in each level give the magic sum of 315;
• the 25 pilars give the magic sum of 315;
• the 20 diagonals through the 5 levels give the magic sum of 315 (e.g. 115+64+38+87+11=315 or 106+44+58+87+20=315);
• the 4 tridiagonals give the magic sum of 315 (e.g. 67+39+63+87+59=315).

Use the same method to construct the panmagic 5x5 square (shift) to construct a symmetric & semi panmagic 5x5x5 cube.

Choose as first row of the first grid in the first level: 2-3-4-0-1. Construct row 2 up to 5 of the first grid of the first level by shifting the first row each time 2 places to the left. Construct the first grid of level 2 up to 5 by shifting the columns of the first grid of the first level each time 2 places to the left.

Choose as first row of the second grid in the first level: 0-1-2-3-4. Construct row 2 up to 5 of the second grid of the first level by shifting the first row each time 2 places to the right. Construct the second grid of level 2 up to 5 by shifting the columns of the second grid of the first level each time 2 places to the left.

The third grid is the same as the second grid, but the levels must be put in reversed order (5 up to 1 instead of 1 up to 5).

Take 1x number from first grid + 5x number from second grid + 25x number from third grid to get a symmetric & semi (pan)magic 5x5x5 cube.

 1x number +1          +    5x number               +    25x number              =    5x5x5 cube, first level 2 3 4 0 1 0 1 2 3 4 3 4 0 1 2 78 109 15 41 72 4 0 1 2 3 3 4 0 1 2 1 2 3 4 0 45 71 77 108 14 1 2 3 4 0 1 2 3 4 0 4 0 1 2 3 107 13 44 75 76 3 4 0 1 2 4 0 1 2 3 2 3 4 0 1 74 80 106 12 43 0 1 2 3 4 2 3 4 0 1 0 1 2 3 4 11 42 73 79 110 1x number +1         +    5x number                +    25x number             =    5x5x5 cube, second level 4 0 1 2 3 2 3 4 0 1 1 2 3 4 0 40 66 97 103 9 1 2 3 4 0 0 1 2 3 4 4 0 1 2 3 102 8 39 70 96 3 4 0 1 2 3 4 0 1 2 2 3 4 0 1 69 100 101 7 38 0 1 2 3 4 1 2 3 4 0 0 1 2 3 4 6 37 68 99 105 2 3 4 0 1 4 0 1 2 3 3 4 0 1 2 98 104 10 36 67 1x number +1         +    5x number                +    25x number             =    5x5x5 cube, third level 1 2 3 4 0 4 0 1 2 3 4 0 1 2 3 122 3 34 65 91 3 4 0 1 2 2 3 4 0 1 2 3 4 0 1 64 95 121 2 33 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 1 32 63 94 125 2 3 4 0 1 3 4 0 1 2 3 4 0 1 2 93 124 5 31 62 4 0 1 2 3 1 2 3 4 0 1 2 3 4 0 35 61 92 123 4 1x nmber +1           +    5x number                +    25x number              =    5x5x5 cube, fourth level 3 4 0 1 2 1 2 3 4 0 2 3 4 0 1 59 90 116 22 28 0 1 2 3 4 4 0 1 2 3 0 1 2 3 4 21 27 58 89 120 2 3 4 0 1 2 3 4 0 1 3 4 0 1 2 88 119 25 26 57 4 0 1 2 3 0 1 2 3 4 1 2 3 4 0 30 56 87 118 24 1 2 3 4 0 3 4 0 1 2 4 0 1 2 3 117 23 29 60 86 1x number +1         +    5x number                +    25x number             =    5x5x5 cube, fifth level 0 1 2 3 4 3 4 0 1 2 0 1 2 3 4 16 47 53 84 115 2 3 4 0 1 1 2 3 4 0 3 4 0 1 2 83 114 20 46 52 4 0 1 2 3 4 0 1 2 3 1 2 3 4 0 50 51 82 113 19 1 2 3 4 0 2 3 4 0 1 4 0 1 2 3 112 18 49 55 81 3 4 0 1 2 0 1 2 3 4 2 3 4 0 1 54 85 111 17 48

Less & extra magic features:

• The vertical diagonals through the levels give not the magic sum;
• The pandiagonals in each level give the magic sum of 315;
• The vertical pandiagonals through the levels give the magic sum of 315
5x5x5, semi [pan]magic 5x5x5 cube.xls