N-dimensional Hypercubes coloring How many ways 3-cube vertices can be coloring using 10 color, vertices which have relation is not able to have same color.
I would also appreciate anyone who show the solution for finding total ways problems in order to color the graphs with more color than chromatic number.

Hint: the chromatic polynomial $P_G(x)$ is such that $P_G(k)$ is equal to the number of ways of properly coloring the vertices of $G$ using $k$ colors. So you want to calculate that for $G=$"$3$-cube" and plug in $k=10$. 
