64 small cubes joined to form a single large cube. The outer surface of the cube is painted by red color. How many of the smaller cubes will not have a colored face?

Answer 1

8 small cubes would make a 2x2x2 cube, all 8 have a colored side, there is no center cube

27 small cubes would make a 3x3x3 cube, 26 would have a colored side, only one cube in the center would remain uncolored.

64 smaller cubes would make a 4x4x4 cube, 8 in the center would remain uncolored.

125 smaller cubes would make a 5x5x5 cube. 3x3x3 = 27 in the center would remain uncolored.

a 216 = 6x6x6 cube would have 4x4x4=64 in the center uncolored