Answer
$\color{blue}{(3z^3+4y^4)(9z^6-12z^3y^4+16y^8)}$
Work Step by Step
With $27z^9=(3z^3)^3$ and $64y^{12}=(4y^4)^3$, the given polynomial is equivalent to:
$=(3z^3)^3+(4y^4)^3$
Factor using the formula $a^3+b^3=(a+b)(a^2-ab+b^2)$ with $a=3z^3$ and $b=4y^4$ to obtain:
$=(3z^3+4y^4)[(3z^3)^2-(3z^3)(4y^4) + (4y^4)^2]
\\=\color{blue}{(3z^3+4y^4)(9z^6-12z^3y^4+16y^8)}$
