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?
Since the entire cube would be painted red, the only cube that will not have at least one side painted red will be the center piece. There is 27 1-inch cubes, and only 1 would not have red, so the answer is \(\color{red} 26\)