  For a number field $\mathbb{K}$, and integral ideals $\mathcal{I}$ and
$\mathcal{J}$ in its number ring $\mathcal{O}_{\mathbb{K}}$, Nowak studied the
asymptotic behaviour of the average of Ramanujan sums
$C_{\mathcal{J}}({\mathcal{I}})$ over both ideals $\mathcal{I}$ and
$\mathcal{J}$. In this article, we extend this investigation by establishing
asymptotic formulas for the second moment of averages of Ramanujan sums over
quadratic and cubic number fields, thereby generalizing previous works of Chen,
Kumchev, Robles, and Roy on moments of averages of Ramanujan sums over
rationals. Additionally, using a special property of certain integral domains,
we obtain second moment results for Ramanujan sums over some other number
fields.
