Let \(\mathbb {K}_3\) be a non-normal field of degree 3 over \( \mathbb {Q}\) . Let \(\ell ,k \ge 2\) be two integers and \( \tau _{k,\mathbb {K}_3}(n)\) denotes the k-dimensional divisor function attached to the coefficients of the Dedekind zeta function in \(\mathbb {K}_3\) . In this paper, we prove an asymptotic result for the following sum \(\begin{aligned} \sum _{\begin{array}{c} n=x_1^2+x_2^2+x_3^2+x_4^2+x_5^2+x_6^2 \le x \\ (x_1,x_2,x_3,x_4,x_5,x_6) \in \mathbb {Z}^6 \end{array}} \tau ^{\ell }_{k,\mathbb {K}_3}(n). \end{aligned}\)
