Suppose that you have a lot of wooden cubes. You decide to decorate them by painting the faces of each cube. You have only two colors of paint, red and blue. Each cube has 6 square faces, and you will paint each face one of these two colors (but a cube may end up with both some red faces and some blue faces). You want to come up with a collection of cubes that are all painted differently. Here, of course, we consider two cubes to be painted the same if one cube can be rotated to look exactly like the other. The question is this: how many different cubes can you design using only these two colors?

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Be sure to include your reasoning with your answer. Good luck!