In the usual setting, the various orientations of the centers are considered irrelevant because you can't tell them apart. So those points in the configuration

In the usual setting, the various orientations of the centers are considered irrelevant because you can't tell them apart. So those points in the configuration space are considered the same point. There is such a thing as a cube with marked centers, sometimes called a supercube, where the difference does matter. These are harder to solve, and I believe God's number is still unknown in that setting.