Let \(K_{3}\) be a non-normal cubic extension over \(\mathbb {Q}\) . And let \(\tau _{k}^{K_{3}}(n)\) denote the k-dimensional divisor function in the number field \(K_{3}/\mathbb {Q}\) . In this paper, we investigate the asymptotic behaviour of higher power moments of \(\tau _{k}^{K_{3}}(n)\) over certain integral binary quadratic forms, which refines and generalizes the recent result in this direction. As an application, we also obtain the asymptotic formula of the variance of the same sequence of coefficients.
