Abstract
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})$ .