Probably won't check back, but, for raising binomials to larger powers than 3, check in a textbook for the binomial expansion theorem. Or, what's perhaps even a little quicker (sometimes) is using Pascal's triangle. (I'll attempt to type it here, but it's too hard to format the spacing)
...................1
.................1..1
...............1..2..1
.............1..3..3..1
...........1..4..6..4..1
.........1..5.10.10.5..1
.......1..6.15.20.15.6..1
continue the pattern, adding adjacent numbers to create the number below them.
These are the coefficients when you expand a binomial
so, (x+y)^6 would be
1x^6 + 6 x^5y + 15 x^4y^2 + 20x^3y^3 +15x^2y^4 + 6xy^5 + 1y^6
now, for a binomial other than (x+y)^n, simply replace "x" with whatever the first term is and replace y with whatever the 2nd term is.
Generally, this is slower for squared or cubed binomials, but can save time when expanding a binomial to the 4th or greater power.