A cube is painted blue on two adjacent surfaces and black on the surfaces opposite to blue surfaces and green on the remaining faces. Now the cube is cut into 216 smaller cubes of equal sizes. Find the number of cubes with no surface painted.

A cube is painted blue on two adjacent surfaces and black on the surfaces opposite to blue surfaces and green on the remaining faces.

Now the cube is cut into 216 smaller cubes of equal sizes. 

If the cube is cut into 216 smaller cubes, then:

Number of small cubes along each edge = $$\sqrt[3]{216} = 6$$

Cubes with no face painted are those that do not lie on the surface of the big cube — i.e., completely internal cubes.​​

​$$(6 - 2)^3 = 4^3 = 64$$

So, 64 cubes have no surface painted.

Thus, the correct answer is (d).