how do you factor m^6-27n^3?
or m^6+27n^3?

First notice that 27 = 3^3. So these equations can be rewritten as the difference of cubes for the first one, and the sum of cubes for the second:


m^6 -27n^3 = (m^2)^3-(3n)^3


and


m^6 +27n^3 = (m^2)^3+(3n)^3


The difference of cubes can be factored like this:


a^3 - b^3 = (a-b)(a^2 +ab+b^2)


and the sum of cubes can be factored like this:


a^3 + b^3 = (a+b)(a^2-ab+b^2)


Hope this helps.