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\left(5r+6\right)\left(25r^{2}-30r+36\right)
Rewrite 125r^{3}+216 as \left(5r\right)^{3}+6^{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 25r^{2}-30r+36 is not factored since it does not have any rational roots.