We make the following observations:
1. Number of cubes with all the three color faces = 2 cubes diagonally opposite to each other.
2. Number of cubes with only same color faces on two faces = three edges without corner cubes = 3*(n-2) = 6
3.Total cubes on the edges = 4*n + 8*(n-2) = 32
4. Number of cubes with only 2 color faces = total cubes on edges – same color on two faces cubes – all three color face cubes = (3) – (2) = 32 – 6 – 2 = 24
5. From the above observation, we can say cubes with only Red and Green faces or only blue and green = 24/3 = 8
6. Number of cubes with exactly one face red = cubes on the two faces of the painted red surface = 2*(n-2)2 = 8
7. Number of cubes with faces only red = (2)/3 + (6) = (n-2) + 2*(n-2)2 = 10
8. Number of cubes with exactly one face painted = 6 faces with (n-2)2 cubes painted on one face = 6*(n-2)2 = 150.
9. Number of cubes with exactly two surfaces painted with different colors = 9 edges with (n-2) cubes = 9*(n-2) = 18
It is a useful approach to make the cube diagram on the paper while solving the question. Cube is a 3-D figure and becomes challenging while solving without a figure, hence it is highly recommended that you make a cube figure while solving the cube questions.
Cubes can also be painted like opposite sides with similar colors or each layer with a different layer. The approach to every kind of question depends upon visualization of the figure. The 2-D diagram would assist a lot in solving but one needs to think more on the three faces hidden in the figure. Cube, being a symmetrical figure allows us to think in symmetrical terms in majority of the questions.