  Assuming the Generalized Riemann Hypothesis for the zeros of the Dirichlet
$L$-functions with characters modulo $q$, we obtain a smoothed version of the
average number of Goldbach representations for numbers which are multiples of a
positive integer $q$. Such an average was first considered by Granville
\cite{Gran07,Gran08} but without any smoothing factor. In this short article,
we also show how the smoothing can be removed.
