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The convolution sum, $\underset{\substack{ {(l,m)\in\mathbb{N}_{0}^{2}}{\alpha\,l+\beta\,m=n} } }{\sum}\sigma(l)\sigma(m)$, where $\alpha\beta=44,52$,is evaluated for all natural numbers $n$. We then use these convolution sums todetermine formulae for the number of representations of a natural number by theoctonary 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 $(a,b)=(1,11),(1,13)$.

Evaluation of the Convolution Sums $\underset{\substack{  {(l,m)\in\mathbb{N}_{0}^{2}} {\alpha\,l+\beta\,m=n} }  }{\sum}\sigma(l)\sigma(m)$, where $\alpha\beta=44,52$