This question helps to focus on some of the properties of cubes and also on systematically combining smaller cubes.
It might be worth having a second cube made of eight smaller cubes available for pupils to be able to count faces and examine how many faces of each smaller cube are visible and the orientation of the cubes and how they fit together before starting on the problem.
There is lots of room for discussion and the use of terms such as "face", "vertex" and "edge" here.

To take this problem a little further, the following questions could be posed:
Can you create a 2x2x2 cube with just two colours on each face?
If you had a 3x3x3 cube made from 27 cubes of three different colours, is it possible to arrange the cubes so that each face has three cubes of each colour visible?
Is it possible to do this in such a way that no row or column contains the same colour twice?

Pupils might like to try Three Cubed and Nine Colours for more of a challenge.