Usually to factor things ,use the remainder and Factor theorem.
Let f(x)=x^3 + 8
try f(1,-1,2,etc) and when you get x=a such that f(a)=0. x-a is a factor of f(x)
For your example; f(-2)=0 so that x+2 is factor of f(x)...you can use synthetic division or long division to get the other factor.