We report on the first search for atmospheric and for diffuse astrophysical
neutrino-induced showers (cascades) in the IceCube detector using 257 days of
data collected in the year 2007-2008 with 22 strings active. A total of 14
events with energies above 16 TeV remained after event selections in the
diffuse analysis, with an expected total background contribution of $8.3\pm
3.6$. At 90% confidence we set an upper limit of
$E^2\Phi_{90%CL}<3.6\times10^{-7} GeV \cdot cm^{-2} \cdot s^{-1}\cdot sr^{-1} $
on the diffuse flux of neutrinos of all flavors in the energy range between 24
TeV and 6.6 PeV assuming that $\Phi \propto E^{-2}$ and that the flavor
composition of the $\nu_e : \nu_\mu : \nu_\tau$ flux is $1 : 1 : 1$ at the
Earth. The atmospheric neutrino analysis was optimized for lower energies. A
total of 12 events were observed with energies above 5 TeV. The observed number
of events is consistent with the expected background, within the uncertainties.
