In this paper, we will investigate three Goldbach–Linnik type problems on cubes of primes. For example, it was proved that, for \(k=1364,\) every pair of sufficiently large even integers can be represented by a pair of eight prime cubes and k powers of 2. In this paper, we give the detailed proof for the first time and sharpen the value of k to 658.

中文翻译：

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素数立方体上的Goldbach–Linnik型问题

在本文中，我们将研究素数立方体上的三个Goldbach-Linnik型问题。例如，证明了，对于\（k = 1364，\），每对足够大的偶数整数都可以由一对八个素数立方体和k个2的幂表示。在本文中，我们给出了第一次并将k的值锐化为658。