Envision two cubes. One embedded within the other. The larger cube is a 10 x 10 x 10 cube. The inner cube must be an 8 x 8 x 8 cube since if we pull out the 8 corner cubes (ones with 4 painted faces) and then the 12 rows of cubes in between the corner cubes from each of the edges, we are left with the paintless cube which runs 8x8x8 cubes in dimension.
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