Abstract
In this study we use some known convolution sums to find the representation number for each of the three octonary quadratic forms
$x_{1}^{2}+x_{2}^{2}+x_{3}^{2}+x_{4}^{2}+6x_{5}^{2}+6x_{6}^{2}+6x_{7}^{2}+6x_{8}^{2}$
,
$2x_{1}^{2}+2x_{2}^{2}+2x_{3}^{2}+2x_{4}^{2}+3x_{5}^{2}+3x_{6}^{2}+3x_{7}^{2}+3x_{8}^{2}$
and
$x_{1}^{2}+x_{2}^{2}+x_{3}^{2}+x_{4}^{2}+3x_{5}^{2}+3x_{6}^{2}+3x_{7}^{2}+3x_{8}^{2}$
.