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