  We report on the search for neutrino-induced particle-showers, so-called
cascades, in the IceCube-40 detector. The data for this search was collected
between April 2008 and May 2009 when the first 40 IceCube strings were deployed
and operational. Three complementary searches were performed, each optimized
for different energy regimes. The analysis with the lowest energy threshold (2
TeV) targeted atmospheric neutrinos. A total of 67 events were found,
consistent with the expectation of 41 atmospheric muons and 30 atmospheric
neutrino events. The two other analyses targeted a harder, astrophysical
neutrino flux. The analysis with an intermediate threshold of 25 TeV lead to
the observation of 14 cascade-like events, again consistent with the prediction
of 3.0 atmospheric neutrino and 7.7 atmospheric muon events. We hence set an
upper limit of $E^2 \Phi_{lim} \leq 7.46\times10^{-8}\,\mathrm{GeV sr^{-1}
s^{-1} cm^{-2}}$ (90% C.L.) on the diffuse flux from astrophysical neutrinos of
all neutrino flavors, applicable to the energy range 25 TeV to 5 PeV, assuming
an $E_{\nu}^{-2}$ spectrum and a neutrino flavor ratio of 1:1:1 at the Earth.
The third analysis utilized a larger and optimized sample of atmospheric muon
background simulation, leading to a higher energy threshold of 100 TeV. Three
events were found over a background prediction of 0.04 atmospheric muon events
and 0.21 events from the flux of conventional and prompt atmospheric neutrinos.
Including systematic errors this corresponds to a $2.7\sigma$ excess with
respect to the background-only hypothesis. Our observation of neutrino event
candidates above 100 TeV complements IceCube's recently observed evidence for
high-energy astrophysical neutrinos.
