The big cube is cut into 4 x 4 x 4 = 64 small cubes

There are 8 original corners - 3 painted sides

There were twelve edges on the original cube - each will give two cubes with two painted sides - 24 in all

There were 6 faces - each with four cubes with one painted side - 24 in all

So the number with no painted sides is 64 - 8 - 24 -24 = 8

(The unpainted cubes formed a small cube 2 x 2 x 2).

OR

no of cubes N = 12 / 3 = 4

**formula: no of cubes having 0 faces painted = ( N - 2 ) ^ 3 **= ( 4 - 2 ) ^ 3 = 2 ^ 3 = 8

similarly **formula for 2 face painted = 12*(N-2)**

for **1 face painted = 6 * ( N - 2 ) ^ 2**

**Option B is the Correct Answer.**