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\left(2s-5t\right)\left(4s^{2}+10st+25t^{2}\right)
Rewrite 8s^{3}-125t^{3} as \left(2s\right)^{3}-\left(5t\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).