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\left(b+4\right)\left(b^{2}-4b+16\right)
Rewrite b^{3}+64 as b^{3}+4^{3}. The sum of cubes can be factored using the rule: p^{3}+q^{3}=\left(p+q\right)\left(p^{2}-pq+q^{2}\right). Polynomial b^{2}-4b+16 is not factored since it does not have any rational roots.