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We find formulae for the number of representation of a positive integer n by each of the quadratic forms x1 + x 2 2 + x 2 3 + x 2 4 + 2x 2 5 + 2x 2 6 + 6x 2 7 + 6x 2 8, x1 + x 2 2 + 2x 2 3 + 2x 2 4 + 2x 2 5 + 2x 2 6 + 3x 2 7 + 3x 2 8, x1 + x 2 2 + 3x 2 3 + 3x 2 4 + 6x 2 5 + 6x 2 6 + 6x 2 7 + 6x 2 8, x1 + x 2 2 + x 2 3 + x 2 4 + 2x 2 5 + 2x 2 6 + 3x 2 7 + 3x 2 8, x1 + x 2 2 + 2x 2 3 + 2x 2 4 + 2x 2 5 + 2x 2 6 + 6x 2 7 + 6x 2 8, x1 + 2x 2 2 + 2x 2 3 + 2x 2 4 + 2x 2 5 + 4x 2 6 + 6x 2 7 + 6x 2 8, 2x1 + 2x 2 2 + 3x 2 3 + 6x 2 4 + 6x 2 5 + 6x 2 6 + 6x 2 7 + 12x 2 8, by using some known convolution sums of divisor functions and known representation formulae for quaternary quadratic forms. Formulae for some other octonary quadratic forms of these type are given before in [4, 5, 6, 11, 17].

Representation number formulae for some octonary quadratic forms