jmc

Each small cube would have dimensions $1\times 1\times 1$ making each cube a unit cube. If there are $16$ cubes per face and there are $5$ faces we are counting, we have $16\times 5=80$ cubes. Some cubes are on account of overlap between different faces. We could reduce this number by subtracting the overlap areas, which could mean subtracting 4 cubes from each side and 12 from the bottom. $80-(4\times 4+12)=80-28=52=\boxed{52}$