Let $N$ be a sufficiently large integer. In this paper, it is proved that, with at most $O(N^{4/9+\epsilon })$ exceptions, all even positive integers up to $N$ can be represented in the form $p_1^2+p_2^3+p_3^3+p_4^3+p_5^3+p_6^3$, where $p_1,p_2,p_3,p_4,p_5,p_6$ are prime numbers.