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\left(m-6\right)\left(m^{2}+6m+36\right)
Rewrite m^{3}-216 as m^{3}-6^{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 m^{2}+6m+36 is not factored since it does not have any rational roots.