what is the factored form of 216p^3+125q^3?

Notice that 216 is a perfect cube and so is 125.
You have the sum of two cubes which is factorable and follows the pattern:

[tex] a^3 + b^3 = (a + b)(a^2 - ab + b^2) [/tex]

[tex] 216p^3 + 125q^3 = [/tex]

[tex] = (6p)^3 + (5q)^3 [/tex]

[tex] = (6p + 5q)(36p^2 - 30pq + 25q^2) [/tex]