Cut Cube

 
Cut Cube

Problem statement:

A solid, four-inch cube of wood is coated with blue paint on all six sides.

Then the cube is cut into smaller one-inch cubes. These new one-inch cubes will have either three blue sides, two blue sides, one blue side, or no blue sides.
 
How many of each will there be?

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There are 8 with three sides colored, 24 with two sides colored, 24 with one side colored, and 8 with no sides colored.