Question 26619
You should be able to recognise this expression as the difference of two cubes, for which the factored form is:
{{{A^3 - B^3 = (A - B)(A^2 + AB + B^2)}}} Applying this to your problem:

{{{27a^3-8b^3 = (3a)^3-(2b)^3}}} and...
{{{(3a)^3-(2b)^3 = (3a-2b)(9a^2+6ab+4b^2)}}} You could go a little farther on the second factor:

{{{(3a-2b)(9a^2+2(2b^2+3ab))}}}