Assignment:
Mrs. Jones had some white paint and some green paint, and a bunch of wooden cubes. Her class decided to paint the cubes by making each face either solid white or green. Juan painted his cube with all six faces white. Julie painted her cube solid green. Herman painted 4 faces white and 2 faces green. How many cubes could be painted in this fashion so that each cube is different from the other? Two cubes are alike if one can be turned so that it exactly matches, color for color on each side, the other cube.
Provide complete and step by step solution for the question and show calculations and use formulas.