This question is based on the information given below: 

The six faces of the cube are painted in a manner that no two adjacent faces have the same colour. The three colours used in painting are red, blue and green. The cube is then cut into 36 smaller cubes in a manner that 32 cubes are of one size and the rest of a bigger size, and each of the bigger cubes has no red side. How many cubes only have one side coloured?

The big cube is cut into 36 small cubes in total. Out of these, 32 are unit cubes and 4 are bigger blocks (each made of 2×2×2=8 unit cubes).

Now, the two outer layers (top and bottom) remain as unit cubes. That’s why we have 32 single-unit cubes there.

Now, these two outer layers are painted red (opposite faces).

We know that a cube has exactly one side coloured if it lies on a face but not on any edge or corner (because edges and corners show 2 or 3 faces).  On each outer red face, the middle 2×2 portion has only the red face painted. That gives four cubes on the top face and four cubes on the bottom face.

So, total cubes with exactly one painted face = 4 + 4 = 8.