  In this paper, we evaluate a smoothed sum of the form $\displaystyle
\sideset{}{^*}\sum_{d \leq X}\left(\sum_{n \leq Y} \left(\frac{8d}{n} \right )
\right)^2$, where $\left ( \frac{8d}{\cdot} \right )$ is the Kronecker symbol
and $\sideset{}{^*}\sum$ denotes a sum over positive odd square-free integers.
