The six faces of a three-inch wooden cube are each painted red. The cube is then cut into one-inch cubes along the lines shown in the diagram. How many of the one-inch cubes have red paint on at least one face?

The six faces of a three-inch wooden cube are each painted red. The cube is then cut into one-inch cubes along the lines shown in the diagram. How many of the one-inch cubes have red paint on at least one face?
I count 26 of them. The cube has been cut into 27 small cubes.
Only the one-inch cube in the very center will have no paint on it.
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