Gozilla's cubes

Consider by cases:

$\textbf{Case 1}$ : 6 white faces

Clearly there is only one cube. 1 possibility.

$\textbf{Case 2}$ : 5 white faces, 1 black face

Every cube of this form is identical, since it can be rotated. 1 possibility.

$\textbf{Case 3}$ : 4 white faces, 2 black faces

Either the two black faces are touching, or they're opposite. 2 possibilities

$\textbf{Case 4}$ : 3 white faces, 3 black faces

The three black faces must either form a corner or a line. 2 possibilities.

By symmetry, the last three cases are the same as the first three.

Thus there are $(1+1+2)*2+2 = \boxed{10}$ different possible paintings.