Earlier I wrote about a 4^6 sudoku cube . This cube can be modified by the introduction of even a further layer. I applied the same stickers to a ckeckered 4x4x4 cube that I made from a black and a white eastsheen 4x4x4. A bunch of further positions showed up that i would regard as solved positions. The attachment below gives a brief overview. It turns out that this cube is now a "supercube": the pairs of centers with identical stickers are now on cubies of different color, so there are no more identical cubies now.