Only the three faces you can see are painted: the top yellow, the front blue and the right side red. After the cube is cut along the lines, how many small cubes carry exactly one colour on exactly one face?

A cube with exactly one painted face lies on one of the three painted faces but not on the edges where two painted faces meet. On each painted 4 by 4 face, removing the row and column that touch the other two painted faces leaves $3\times 3=9$. Three faces: $3\times 9=27$.