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\left(B-2c\right)\left(B^{2}+2Bc+4c^{2}\right)
Rewrite B^{3}-8c^{3} as B^{3}-\left(2c\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).