I am so sorry for misleading you. I needed to solve this problem, because it occurred to me whilst I was solving another one. Indeed, what I had written is not true. In such case, could you help me find all integers $\displaystyle n >= 1 $ for which

$\displaystyle 1+2^{n+1} + 2^{2n+2}$

i divisible by

$\displaystyle 1+2^{n} + 2^{2n}$?