If you are asking how to solve an equation like a^3+b^3=0, you have to factor the equation first. The equation for factoring a sum of perfect cubes is as follows:
a^3+b^3= (a+b)(a^2-2ab+b^2)
From there, you set (a+b) equal to 0 and (a^2-2ab+b^2) equal to zero and find your three different answers (or at least there should be three answers). If you can factor the second parenthesis even more, do so and set both inserts equal to zero...
IF that makes any sense at all