what does factoring the sum or difference of two cubes mean

Answer 1

It means using the handy known factorizations, as in

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

Of course, only the sum is needed, since
(a^3-b^3) = (a^3+(-b)^3)

once you recognize the sum of two cubes, like

125x^6+216/z^9
where
a = 5x^2
b = 6/z^3
just plug into the formula

125x^6 + 216/z^9 = (5x^2+6/z)(25x^4-30x^2/z^3+36/z^6)

so, it helps to know your cubes of small numbers, and watch for exponents which are multiples of 3.