中文摘要：

利用三角和方法以及经典高斯和的性质研究三次高斯和与二项指数和混合均值的计算问题，并借助于三次特征的特殊性给出了该混合均值的一个有趣的三阶线性递推公式。应用该递推公式，完全解决了一类三次高斯和与二项指数和混合均值的计算问题。

英文摘要：

Using the trigonometric sums method and the properties of the classical Gauss sums to study the computational problem of the hybrid power mean involving the cubic Gauss sums and two-term exponential sums, and with the aid of the properties of 3th character an interesting three-order linear recurrence formula for it is given. Applying this recurrence formula, the compu- tational problem of one kind hybrid power mean involving the cubic Gauss sums and two-term ex- ponential sums is completely solved..