An analysis of the (coloredcubes)3 puzzle

Start with a collection of cubes and a palette of six colors. We paint the cubes so that each cube face is one color, and all six colors appear on every cube. Take n3n3 cubes colored in this manner. When is it possible to assemble these cubes into an n×n×nn×n×n large cube so that each face on the large cube is one color, and all six colors appear on the cube faces? For the 2×2×22×2×2 case we give necessary and sufficient conditions for a set of eight cubes to have a solution. Furthermore, we show that the (coloredcubes)3 puzzle always has a solution for n>2n>2.