\(4n\) Cubes

Discrete Mathematics Level pending

You have \(4n\) cubes, \(n>7\), that can have eight different colors, and you arrange them into a \(2 \times 2 \times n\) cuboid, so that no two cubes of the same color meet at a side, an edge or a vertex.

Lets take the colors to be - red, orange, yellow, green, blue, teal, cyan and magenta.

Given that the four cubes on one end are red, orange, yellow, and green, how many ways are there of coloring four cubes on the other end?

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