A cube of side 5 cm is painted on all its side. If it is sliced into 1 cubic cm cubes, how many 1 cubic cm cubes will have exactly one of their sides painted?     

Imagine just one face of the 5x5 cube. (I'm imagining this massive Rubik's cube Which of the 1x1 cubes will have paint on only one face? Only those which are not on the edges - these will share a painted face with another side. The cubes that are not part of the edge form a 3x3 grouping of 1cm cubes. Therefore each face has 9 cubes that are painted one color. Since there are 6 faces we get 6x9 = 54.