Problem 9 (2020 AMC 8)

Akash's birthday cake is in the form of a $4\times4\times4$ inch cube. The cake has icing on the top and the four side faces, and no icing on the bottom. Suppose the cake is cut into $64$ smaller cubes, each measuring $1\times1\times1$ inch, as shown below. How many of the small pieces will have icing on exactly two sides? [See figure in original PDF]