Answer
$(x^2+2y)(x^4-2x^2y+4y^2)$
Work Step by Step
The formula for factoring the sum of two cubes is: $A^3+B^3=(A+B)(A^2-AB+B^2)$.
The formula for factoring the difference of two cubes is: $A^3-B^3=(A-B)(A^2+AB+B^2)$.
Hence here: $x^6+8y^3=\\=(x^2)^3+(2y)^3\\=(x^2+2y)((x^2)^2-x^2\cdot2y+(2y)^2)\\=(x^2+2y)(x^4-2x^2y+4y^2)$