  In this paper, we use a modular form approach to evaluate the convolution
sums $\sum_{l+42m=n}\sigma (l)\sigma (m)$, $\sum_{2l+21m=n}\sigma (l)\sigma
(m),$ $\sum_{3l+14m=n}\sigma (l)\sigma (m)$ and $\sum_{6l+7m=n}\sigma (l)\sigma
(m) $ for all positive integers $n\mathbf{,}$ and then use their evaluations to
determine the number of representation of a positive integer $n$ by the
quadratic form $x_{1}^{2} +x_{1}x_{2} +x_{2}^{2} +x_{3}^{2} +x_{3}x_{4}
+x_{4}^{2} + 14(x_{5}^{2} +x_{5}x_{6} +x_{6}^{2} +x_{7}^{2} +x_{7}x_{8}
+x_{8}^{2})$.
