if you will divide a cube into 125 pieces each face will have 25 cubes ( to understand to divide a surface into 25 pieces you will need a 5x5 grid, hence for 3 dimensions i.e. cube you will have to find the cube-root of 125 i.e. 5 so each face will have 25 faces. ) out of which the one at edges will have at least 2 sides painted, then the remaining cubes will be 9 at the center of each face whose at least one face will be painted, if you will remove these painted cubes from each side, you'll get a cube with 3 x 3 cubes on each face multiplied by 3 by the same logic as before, you'll get 27 cubes which are not painted.