#### Answer

(3m-1)(9m$^2$+3m+1)

#### Work Step by Step

27x$^3$-1
This expression is a difference of cubes. If a is the cube root of the first term and b is the cube root of the second term, the factorization is
(a-b)(a$^2$+ab+b$^2$.
$\sqrt[3] {27m^3}$=3m and
$\sqrt[3] 1$=1. So the factorization is
(3m-1)(9m$^2$+3m+1).