Answer
$\color{blue}{(3-m-2n)(9+3m+6n+m^2+4mn+4n^2)}$
Work Step by Step
With $27=3^3$, the given polynomial is equivalent to:
$=3^3-(m+2n)^3$
Factor using the formula $a^3-b^3=(a-b)(a^2+ab+b^2)$ with $a=3$ and $b=m+2n$ to obtain:
$=[3-(m+2n)][3^2+3(m+2n) + (m+2n)^2]
\\=(3-m-2n)[9+3m+6n+(m^2+4mn+4n^2)]
\\=\color{blue}{(3-m-2n)(9+3m+6n+m^2+4mn+4n^2)}$
