Since "cubes" with higher dimension than three exist i think its natural to ask for higher dimensional Rubikscubes. These so called hypercubes dont seem the have been discribed from a group theoretic point of view.

Are there any papers on this? Is the group of the $3\times 3\times 3 \times 3$ cube a subsgroup a wreath product of another wreath product?

In case you dont know about the $3\times 3\times 3$ cube.Its group is a subgroup of a direct group of wreath products.The wreath products discribing the corner pieces and the edge pieces and representing a permutation of them with its action in the respective orientation.Thats why i conjecture that in the $3\times 3\times 3 \times 3$ case we might will get a wreath product of the permutation of the faces,which are now 3d cubes itself,by the the wreath product of the permutation of the 2d faces of these by the groups of thier orientations.