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\left(4z-9\right)\left(16z^{2}+36z+81\right)
Rewrite 64z^{3}-729 as \left(4z\right)^{3}-9^{3}. The difference of cubes can be factored using the rule: a^{3}-b^{3}=\left(a-b\right)\left(a^{2}+ab+b^{2}\right). Polynomial 16z^{2}+36z+81 is not factored since it does not have any rational roots.