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