A Cubical grid

Consider the 512 points \( (x, y, z ) \) with integer coordinates, where \( 1 \leq x, y, z \leq 8 \).

How many cubes are there such that their vertices lie in the set of these points, and at least one of their faces is parallel to the \(xy, yz,\) or \(zx \) plane?

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