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 3.6E^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 and that the flavor composition of the flux is 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.

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