Answer
$a^3-27=(a-3)(a^2+3a+9)$
Work Step by Step
The given expression can be written as:
$=a^3-3^3$
RECALL:
A sum or difference of two cubes can be factored using the following:
(i) $a^3-b^3=(a-b)(a^2+ab+b^2)$
(ii) $a^3+b^3 = (a+b)(a^2-ab+b^2)$
Use formula (1) above with $a=a$ and $b=3$ to have:
$=(a-3)(a^2+(a)(3)+3^2]
\\=(a-3)(a^2+3a+9)$