Answer
$(x-y)(x^2+xy+y^2-1)$
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: $x^3-y^3-x+y=\\=(x-y)(x^2+xy+y^2)-(x-y)\\=(x-y)(x^2+xy+y^2-1)$