qqwref
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Just thinking about the solution a little...
Each piece must be on all 6 faces and appears exactly 3 times in the cube, so using some basic math the possibilities must be:
- two corners, one middle center (one color)
- one corner, one edge, one center (six colors)
- three edges (two colors)
One possible solution:
EDIT: Haha, this looks suspiciously like Stefan's solution 
- two corners, one middle center (one color)
- one corner, one edge, one center (six colors)
- three edges (two colors)
One possible solution:
Code:
041 638 275
527 104 863
386 752 410