An allocation feasible for the grand coalition, $(u_1,\ldots,u_N)$ such that $\sum_nu_n\leq \nu(\mathcal N)$, is blocked by coalition $S$ if $\nu(S)>\sum_{n\in S}u_n$. The core is the set of unblocked allocations.
Suppose $\mathcal N=\{1,2,3\}$. $\nu(\{i\})=0$, $\nu(\{i,j\})=a$ and $\nu(\mathcal N)=b$. The game is superadditive if $b>a>0$. If $(y_1,y_2,y_3)$ is in the core, then for all pairs $i,j$, \begin{equation*} y_i+y_j\geq a \end{equation*} Summing over the three pairs, \begin{equation*} 2(y_1+y_2+y_3)>3a\end{equation*} For the core to exist, $b\geq 3a/2$. Existence of the core requires more than superadditivity.