$\displaystyle (a - b)^3 - b^3$
$\displaystyle [(a - b) - b][(a - b)^2 + (a - b)b + b^2]$
Is that right?
$\displaystyle 27a^3 - 1 = (3a)^3 - (1)^3$
and
$\displaystyle x^3 - y^3 = (x - y)(x^2 + xy + y^2)$
So let $\displaystyle x = 3a$ and $\displaystyle y = 1$
Thus
$\displaystyle 27a^3 - 1 = (3a)^3 - (1)^3 = (3a - 1)((3a)^2 + (3a)(1) + (1)^2)$
$\displaystyle = (3a - 1)(9a^2 + 3a + 1)$
-Dan