Powers of 2 in two Goldbach-Linnik type problems involving prime cubes

In this paper, we show that every sufficiently large even integer can be represented as eight prime cubes and k1 powers of 2, and every pair of sufficiently large even integers can be represented as a pair of eight prime cubes and k2 powers of 2, where k1=28 and k2=98. These results improve previous results k1=30 and k2=335, respectively.