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3\left(x^{3}+64\right)
Factor out 3.
\left(x+4\right)\left(x^{2}-4x+16\right)
Consider x^{3}+64. Rewrite x^{3}+64 as x^{3}+4^{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).
3\left(x+4\right)\left(x^{2}-4x+16\right)
Rewrite the complete factored expression. Polynomial x^{2}-4x+16 is not factored since it does not have any rational roots.