The convolution sum P (l,m)2N2 0 l+ m=n (l)(m), where = 48 and = 64, is elementarily evaluated for all natural numbers n. The evaluation of the convolution sums for these levels is achieved using the sum of divisors function, primitive Dirichlet characters and modular forms. The evaluation of these convolution sums is then used to determine formulae for the number of representations of a natural number by the octonary quadratic forms a (x2 1 + x2 2 + x2 3 + x2 4) + b (x2 5 + x2 6 + x2 7 + x2 8) and c (x2 1 + x1x2 + x2 2 + x2 3 + x3x4 + x2 4) + d (x2 5 + x5x6 + x2 6 + x2 7 + x7x8 + x2 8), where (a, b) = (1, 12), (1, 16), (3, 4) and (c, d) = (1, 16).
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