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\left(2m-3k\right)\left(4m^{2}+6km+9k^{2}\right)
Rewrite 8m^{3}-27k^{3} as \left(2m\right)^{3}-\left(3k\right)^{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).