I can't think how to do this with groups, but there is a sort of brute-force solution. Set all of the pivot points of the small cubes to the center of the entire cube. Then, when you're animating, just select the side you want and rotate them. They should rotate about the absolute center of the entire cube. You'll definitely have to edit the fcurves on them. One of my students did an entire Rubik's cube animation this way. Very quick and easy to work with.