Vertices of Cube coloured with black or white colour In how many rotionally distinct ways can the vertices of a cube be coloured with black or white colour ?
I don't know how to approach this question. Please provide some insight.

You can still use Burnside's Lemma for coloring the vertices, because the group of symmetric rotations of a cube (where |G| = 24) acts on the set of vertices, as well as the set of faces.
The "identity rotation" leaves all 2^8 possibilities untransformed so that will be the first term in the summation,  and then the total will be divided by 24, the number of symmetric rotations on a cube.
So (16^2 + 6 * 4 + 3 * 16 + 8 * 16 + 6 * 16)/24
= 1/3 * (32+3+6+16 +12) = 69/3 = 23
(unless I've  counted wrong or done the math wrong,  but since I came up with an integer, I tend to think that I got it right. )
