To answer this question, you have to remember that you can't distribute a power the same way you can distribute multiplication and division. So (x+8)3 is the same as (x+8)(x+8)(x+8).
Then you multiply it out, and it looks like
You do this by multiplying each of the numbers in each binomial by each of the other numbers, so first you do x*x*x, then x*x*8, then x*8*x, and so on.
Simplified, this looks like
Hope this helped!