I have several boxes, each containing a number of cubes. Each cube has black and white faces (at least one of each colour per cube), and each box contains all possible different cubes, with no duplicates, My three nephews opened the first box and each tried to assemble their own 2x2x2 cube with only one colour on its outer faces, and of course they failed. They then opened further boxes until they were each able to assemble a single-coloured 2x2x2 cube. They then put all the leftover cubes from the open boxes in a pile. How many cubes were there in the leftover pile?
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