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[Thermopyle] Since the question has been asked in such a way so as to cross the boundaries of both physics and mathematics - so must the answers.
A cube is both a mathematical concept and something that can exist in the real world. Space and time are inexorably linked, they may not have the same properties, and they certainly don't act in the same way, but it is interesting to think along these lines.
However, to properly answer the question, we all need to agree on what a cube is, what space is, and what time is. And until we've got that covered, we really don't have a chance at providing a mutually acceptable answer.
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