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For all natural numbers $n$, we discuss the evaluation of the convolutionsum, $\underset{\substack{{(l,m) \in \mathbb{N}_0^2} \\ {\alpha\,l+\beta\,m=n}} }{\sum}\sigma(l)\sigma(m)$, where $\alpha\beta=14,22,26$. We generalize theextraction of the convolution sum using Eisenstein forms of weight $4$ for allpairs of positive integers $(\alpha,\beta)$. We also determine formulae for thenumber of representations of a positive integer by the octonary quadratic forms$a\,(x_1^2 + x_2^2 + x_3^2 + x_4^2)+ b\,(x_5^2 + x_6^2 + x_7^2 + x_8^2)$, where$(a,b)= (1,1), (1,3), (2,3), (1,9)$. These numbers of representations of apositive integer are applications of the evaluation of certain convolution sumsby J. G. Huard et al., A. Alaca et al. and D. Ye.

Evaluation of the Convolution Sum involving the Sum of Divisors Function for 14, 22 and 26