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\left(4x-9\right)\left(16x^{2}+36x+81\right)
Rewrite 64x^{3}-729 as \left(4x\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 16x^{2}+36x+81 is not factored since it does not have any rational roots.