Rubik's Cubes? Lets upgrade to Cube21 sided solvers
I couldn't solve the easy version of the Rubik's cube, maybe with a hammer I'll be able to solve the Cube21 sided version. Pavel Šavara however solved the Cube21 programmatically with C++, CLI, WPF, SQL, WCF, and ASP + Ajax. Pavel goes into some detail on his methods and math on his blog post.
He also gives out the source code for his program.
Update: After talking with Pavel, he said the Rubik's cube is a far harder problem to solve. Here is a wikipedia entry on it.