find a power series that reps 1/(1+x)^3 on the interval -1,1

now we know that 1/(1+x)= x^0-x^1+x^2-x^3+x^4-x^5+...

and I originally thought that I could cube each term to get

1/(1+x)^3=x^0-x^3+x^6-x^9+x^12-x^15+...

to get the p series = Sigma(n=0,infinity)[(-1)^n*x^(3n)]

but this I am not 100% sure of. Any tips?