#### Answer

$\color{blue}{(1-3x^2)(1+3x^2+9x^4)}$

#### Work Step by Step

With $27x^6=(3x^2)^3$ and $1=1^3$, the given expression is equivalent to:
$=1^3-(3x^2)^3$
Factor using the formula $a^3-b^3=(a-b)(a^2+ab+b^2)$ with $a=1$ and $b=3x^2$ to obtain:
$=(1-3x^2)[1^2+1(3x^2)+(3x)^2]
\\=\color{blue}{(1-3x^2)(1+3x^2+9x^4)}$