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27\left(z^{3}+27y^{3}\right)
Factor out 27.
\left(3y+z\right)\left(9y^{2}-3yz+z^{2}\right)
Consider z^{3}+27y^{3}. The sum of cubes can be factored using the rule: a^{3}+b^{3}=\left(a+b\right)\left(a^{2}-ab+b^{2}\right).
27\left(3y+z\right)\left(9y^{2}-3yz+z^{2}\right)
Rewrite the complete factored expression.