The six faces of a cube are painted black. The cube is then cut into $5^3 = 125$ smaller cubes, all the same size. How many of the smaller cubes do not have any black faces?

There are (5 - 1)^3 = 64 cubes that do not hav any black faces.

Incorrect

(5-2)^3 = 3^3 = 27 do not have any paint on them