jmc

The number of painted faces is $9(6)=54$. However, the four edge faces painted on each face are also painted on the other face. Thus $4(6)=24$ of the painted faces are on cubes with two painted faces. These account for only $12$ painted cubes, in addition to the $54-24=30$ singly painted cubes. So there are $42$ painted cubes, leaving $125-42=\boxed{83}$ unpainted cubes.