On the Waring-Goldbach Problem for Six Cubes and Two Biquadrates

Let P_r denote an almost prime with at most r prime factors, counted according to multiplicity. In the present paper, it is proved that for any sufficiently large even integer n, the equation

$$n = {x^3} + p_1^3 + p_2^3 + p_3^3 + p_4^3 + p_5^3 + p_6^4 + p_7^4$$

has solutions in primes p_i with x being a P₆. This result constitutes a refinement upon that of Hooley C.