Total colorings without considering rotations: Each face of the cube can be either black or white, so there are $2^6 = 64$ possible colorings if we don't consider rotations.

Accounting for rotations: A cube has 24 different rotations, so many of the 64 colorings are identical when rotated.

Distinct colorings: After accounting for all rotations, the number of distinct colorings is 10.

So, the correct answer is B. 10.