Let me get this right. Are we talking about writing an integer on each of the 9 labels on each side of a Rubik’s cube to form six magic squares, then scrambling the cube and reconstructing the original? Sure, that has already been done.
The problem that immediately sprang to my mind is “how do we know there is a unique solution once scrambled?”, though intuitively there are too many constraints for there being more than one. This is a surmise, not a fact. In the example above all the squares are identical (the famous Lo Shu configuration well known to recreational maths buffs) but integers could be totally different on each label. They could also be negative for what is worth. And the 6 and 9 could be flipped and mistaken for each other, as group rotations change the orientation of labels. Hmm.