Abstract
In this study we derive formulae for the number of representations of n by the octonary quadratic forms
$x_{1}^{2}+x_{1}x_{2}+x_{2}^{2}+2x_{3}^{2}+2x_{3}x_{4}+2x_{4}^{2}+2x_{5}^{2}+2x_{5}x_{6}+2x_{6}^{2}+4x_{7}^{2}+4x_{7}x_{8}+4x_{8}^{2}, x_{1}^{2}+x_{1}x_{2}+x_{2}^{2}+2x_{3}^{2}+2x_{3}x_{4}+2x_{4}^{2}+3x_{5}^{2}+3x_{5}x_{6}+3x_{6}^{2}+6x_{7}^{2}+6x_{7}x_{8}+6x_{8}^{2}, x_{1}^{2}+x_{1}x_{2}+x_{2}^{2}+2x_{3}^{2}+2x_{3}x_{4}+2x_{4}^{2}+4x_{5}^{2}+4x_{5}x_{6}+4x_{6}^{2}+8x_{7}^{2}+8x_{7}x_{8}+8x_{8}^{2}$
for any n ∈ ℕ0.