A cube is coloured red on all of its faces. It is then cut into 64 smaller cubes of equal size. Which of the following statements are correct?
(A) The number of smaller cubes with two surfaces painted is 36.
(B) The number of smaller cubes with one surface painted is 24.
(C) The number of smaller cubes with no surface painted is 8.
(D) The number of smaller cubes with at least two surfaces painted is 30.

If a bigger cube is initially painted, and cut into $$n^3$$ smaller cubes, then - 
Number of cubes with 3 faces painted = $$8$$
Number of cubes with 2 faces painted = $$12(n-2)$$
Number of cubes with 1 face painted = $$6(n-2)^2$$
Number of cubes with no face painted = $$(n-2)^3$$

A cube is coloured red on all of its faces. It is then cut into 64 smaller cubes of equal size. Thus, the value of $$n=4$$.
Number of cubes with 3 faces painted = $$8$$
Number of cubes with 2 faces painted = $$12(n-2)=24$$
Number of cubes with 1 face painted = $$6(n-2)^2=24$$
Number of cubes with no face painted = $$(n-2)^3=8$$
Number of cubes with atleast 2 faces painted = $$24+8=32$$

Thus, only (B) and (C) are correct.