Its always difficult to find the factors, given the simplest form.

a^3 - b^3 is (a-b)(a^2 + ab + b^2).

If one of the factors is known, it becomes a bit easier.

For lower degrees, by remembering some formulae, it can be done easily.

Like a^2 - b^2 = (a+b) x (a-b),

(a^3 + b^3) = (a+b) x (a^2 - ab + b^2) etc.

When you are aksed to prove that the LHS is equal to the RHS,

it is always better to start with lower degrees.