Complex Numbers

If $\omega$ is a complex cube root of unity, then the value of the expression $2\left(1+\dfrac{1}{\omega}\right)\left(1+\dfrac{1}{\omega^2}\right) + 3\left(2+\dfrac{1}{\omega}\right)\left(2+\dfrac{1}{\omega^2}\right) + \ldots + (n+1)\left(n+\dfrac{1}{\omega}\right)\left(n+\dfrac{1}{\omega^2}\right)$ is...