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We evaluate the convolution sums $\sum_{l,m\in {\mathbb N}, {l+15m=n}}\sigma(l) \sigma(m)$ and $\sum_{l,m\in {\mathbb N}, {3l+5m=n}} \sigma(l)\sigma(m)$ for all $n\in {\mathbb N}$ using the theory of quasimodular formsand use these convolution sums to determine the number of representations of apositive integer $n$ by the form $$ x_1^2 + x_1x_2 + x_2^2 + x_3^2 + x_3x_4 +x_4^2 + 5 (x_5^2 + x_5x_6 + x_6^2 + x_7^2 + x_7x_8 + x_8^2). $$ We alsodetermine the number of representations of positive integers by the quadraticform $$ x_1^2 + x_2^2+x_3^2+x_4^2 + 6 (x_5^2+x_6^2+x_7^2+x_8^2), $$ by usingthe convolution sums obtained earlier by Alaca, Alaca and Williams \cite{{aw3},{aw4}}.

Evaluation of the convolution sums $\sum_{l+15m=n} \sigma(l) \sigma(m)$ and $\sum_{3l+5m=n} \sigma(l) \sigma(m)$ and some applications