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\left(4x+5\right)\left(16x^{2}-20x+25\right)
Rewrite 64x^{3}+125 as \left(4x\right)^{3}+5^{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). Polynomial 16x^{2}-20x+25 is not factored since it does not have any rational roots.