  The first data from the LHC Run-2 have shown a possible excess in diphoton
events with invariant mass $\sim 750$ GeV, suggesting the existence of a new
resonance which may decay dominantly into dark matter (DM) particles. We show
in a simple model that the reported diphoton excess at the LHC is consistent
with another photon excess, the $2$ GeV excess in cosmic gamma-ray fluxes
towards the Galactic Center observed by the Fermi-LAT. Both the excesses can be
simultaneously explained by a $\sim 60$ GeV scalar DM particle annihilating
dominantly into two gluons with a typical thermal annihilation cross section,
which leads to the prediction of a large width to mass ratio $\Gamma/M\approx
\mathcal{O}(10^{-2})$ of the resonance. The upper limit on the dijet search at
LHC Run-1 leads to a $lower$ limit on the predicted cross section for DM
annihilating into $\gamma\gamma$ final states $\langle\sigma
v\rangle_{\gamma\gamma}
\gtrsim\mathcal{O}(10^{-30})~\mbox{cm}^{3}\mbox{s}^{-1}$. Both the predictions
can be tested by the LHC, Fermi-LAT and future experiments.
