Consider a positive odd integer $N>1$ of form
$N=T^2+27U^2, T,U\in\mathbb{Z}, T, U\neq 0$
which cannot be divided by 3.
Question: Suppose N can be divided by a prime number $p$, $p\equiv1(mod 3)$. Is it possible that $p={T_0}^2+27{U_0}^2,T_0,U_0\in\mathbb{Z}$?