  The IceCube neutrino observatory has established the existence of a flux of
high-energy astrophysical neutrinos inconsistent with the expectation from
atmospheric backgrounds at a significance greater than $5\sigma$. This flux has
been observed in analyses of both track events from muon neutrino interactions
and cascade events from interactions of all neutrino flavors. Searches for
astrophysical neutrino sources have focused on track events due to the
significantly better angular resolution of track reconstructions. To date, no
such sources have been confirmed. Here we present the first search for
astrophysical neutrino sources using cascades interacting in IceCube with
deposited energies as small as 1 TeV. No significant clustering was observed in
a selection of 263 cascades collected from May 2010 to May 2012. We show that
compared to the classic approach using tracks, this statistically-independent
search offers improved sensitivity to sources in the southern sky, especially
if the emission is spatially extended or follows a soft energy spectrum. This
enhancement is due to the low background from atmospheric neutrinos forming
cascade events and the additional veto of atmospheric neutrinos at declinations
$\lesssim-30^\circ$.
