[3x3x3x3]  Including mirrorring and/or rotating there are 22.272 possible (simple) 3x3x3x3

magic cubes. You need 2 out of 28 different grids. There are 348 combination

possibilities. For each grid you can use 1 of the 8 magic 3x3 squares (n.b.: 348

x 8 x 8 = 22.272).

[4x4x4x4]  You can construct a 4x4x4x4 pantriagonal and panquadragonal cube.

[5x5x5x5]  You can construct a 5x5x5x5, which is (two dimensional) panmagic in the levels or a 5x5x5x5 pantriagonal cube. 

[6x6x6x6] You can construct a simple 6x6x6x6 magic cube.

[7x7x7x7]  You can construct a 7x7x7x7, which is (two dimensional) panmagic in the levels or a 7x7x7x7 pantriagonal cube.

 [8x8x8x8]  You can construct a 8x8x8x8 pantriagonal and panquadragonal magic cube. 
 
[9x9x9x9]  You can construct a 9x9x9x9 pantriagonal magic cube or a 9x9x9x9 panquadragonal magic cube.

[10x10x10x10] You can construct a simple 10x10x10x10 magic cube.

[11x11x11x11]  You can construct a pantriagonal & pantriagonal 11x11x11x11 magic cube, which is also panmagic in the levels and half pandiagonal magic through the levels.

[12x12x12x12]  You can construct a 12x12x12x12 pantriagonal and panquadragonal magic cube.

[13x13x13x13]   You can construct a pantriagonal & pantriagonal 13x13x13x13 magic cube, which is also panmagic in the levels and half pandiagonal magic through the levels.

[14x14x14x14] You can construct a simple 14x14x14x14 magic cube.

[15x15x15x15]   You can construct a pantriagonal & pantriagonal 15x15x15x15 magic cube, which is also panmagic in the levels and half pandiagonal magic through the levels.

 
[16x16x16x16]  You can construct a 16x16x16x16 most perfect (= more than Nasik) tesseract.