Infinite Sequences and Series · Superchallenge problem

Positive real numbers $a$ and $r$ with $0<r<1$ satisfy $\displaystyle\sum_{n=0}^{\infty}ar^n=10$ and $\displaystyle\sum_{n=0}^{\infty}ar^{2n}=6$. Find the exact value of $\displaystyle\sum_{n=0}^{\infty}ar^{3n}$.