Answer
$(x^{2}-2y)(x^{4}+2x^{2}y+4y^{2})$
Work Step by Step
$x^{6}-8y^{3}=(x^{2})^{3}-(2y)^{3}=(x^{2}-2y)[(x^{2})^{2}+(x^{2})(2y)+(2y)^{2}]=(x^{2}-2y)(x^{4}+2x^{2}y+4y^{2})$
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