Answer
$(x^3-1)(x^6+x^3+1)$
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: $x^9-1=\\=(x^3)^3-(1)^3\\=(x^3-1)((x^3)^2+x^3\cdot 1+(1)^2)\\=(x^3-1)(x^6+x^3+1)$