Abstract
Let N(a1, …, a4; n) denote the number of representations of an integer n by the form
$a_{1}(x_{1}^{2}+x_{1}x_{2}+x_{2}^{2})+a_{2}(x_{3}^{2}+x_{3}x_{4}+x_{4}^{2})+a_{3}(x_{5}^{2}+x_{5}x_{6}+x_{6}^{2})+a_{4}(x_{7}^{2}+x_{7}x_{8}+x_{8}^{2})$
. In this paper we derive formulae for N(1, 1, 1, 2; n) and N(1, 2, 2, 2; n). These formulae are given in terms of σ3(n).