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Jan 19, 2023 at 0:55 vote accept Chuck Liu
Jan 18, 2023 at 14:32 comment added Max Alekseyev @ChuckLiu: Then magic squares become irrelevant. Think of them as colors and thus one need to enumerate independent colorings of the cube faces. Solution to this problem is well known, even if we count colorings up to rotations of the cube.
Jan 18, 2023 at 5:58 comment added Chuck Liu I assume the six sides (up, down), (left, right), (forward, backward). For (up, down), we can get 8 combinations. So I think the number of combination is between from $8$ to $8^3$.
Jan 15, 2023 at 16:48 comment added Max Alekseyev @ChuckLiu: I don't see much clarification with respect to cube filling. Does my interpretation match your intended question for $n=3$?
Jan 14, 2023 at 23:39 comment added Chuck Liu Thanks for your answer. I have clarified my question.
Jan 14, 2023 at 15:14 history edited Max Alekseyev CC BY-SA 4.0
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Jan 14, 2023 at 12:55 history answered Max Alekseyev CC BY-SA 4.0