Power series for the rational function $(1+x)^3/(1-x)^3$ 
Show that $$\dfrac{(1+x)^3}{(1-x)^3} =1 + \displaystyle\sum_{n=1}^{\infty} (4n^2+2)x^n$$

I tried with the partial frationaising the expression that gives me 
$\dfrac{-6}{(x-1)} - \dfrac{12}{(x-1)^2} - \dfrac{8}{(x-1)^3}  -1$ 
how to proceed further on this having doubt with square and third power term in denominator.

Hint: Differentiate the series: $\dfrac{1}{1-x} = 1+x+x^2+\cdots$, and differentiate it again.
