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2\left(8y^{3}+x^{3}\right)
Factor out 2.
\left(x+2y\right)\left(x^{2}-2xy+4y^{2}\right)
Consider 8y^{3}+x^{3}. Rewrite 8y^{3}+x^{3} as x^{3}+\left(2y\right)^{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).
2\left(x+2y\right)\left(x^{2}-2xy+4y^{2}\right)
Rewrite the complete factored expression.