Answer
$(2x+y)(x^2+xy+y^2)$
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: $x^3+(x+y)^3=\\=(x+x+y)((x^2-x\cdot(x+y)+(x+y)^2)\\=(2x+y)(x^2-x^2-xy+x^2+2xy+y^2)\\=(2x+y)(x^2+xy+y^2)$
