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We evaluate the convolution sum $\displaystyle W_{a,b}(n):= \sum_{al+bm=n}\hspace{-3mm} \sigma(l) \sigma(m)$ for $(a,b)=(1,28), (4,7), (2,7)$ for allpositive integers $n$. We use a modular form approach. We also re-evaluate theknown sums $W_{1,14}(n)$ and $W_{1,7}(n)$ with our method. We then use theseevaluations to determine the number of representations of $n$ by the octonaryquadratic form $x_1^2 + x_2^2 +x_3^2 + x_4^2 + 7(x_5^2 + x_6^2 + x_7^2 +x_8^2)$. Finally we compare our evaluations of the sums $W_{1,7}(n)$ and$W_{1,14}(n)$ with the evaluations of Lemire and Williams [10] and Royer [13]to express the modular forms $\Delta_{4,7}(z)$, $\Delta_{4,14, 1}(z)$ and$\Delta_{4,14, 2}(z)$ (given in [10, 13]) as linear combinations of etaquotients.

The convolution sum $\sum_{al+bm=n} \sigma(l) \sigma(m)$ for $(a,b)=(1,28), (4,7), (1,14), (2,7), (1,7)$