Neutrino detectors, such as IceCube, can be used to perform indirect dark matter searches. Under the assumption that dark matter annihilates or decays, e.g. for the Weakly Interacting Massive Particles (WIMPs) scenarios, Standard Model particles are expected to be created by its annihilation or decay. These Standard Model particles could in turn produce neutrinos detectable by neutrino telescopes. As our Galaxy is believed to be embedded in a halo of dark matter whose density increases towards its centre, the Galactic Centre represents an ideal target for indirect searches, with the strongest dark matter annihilation signal at Earth being expected from this direction. In this contribution, the results of a dark search towards higher energies are presented, along with the sensitivities of a low energy indirect search for dark matter in the Galactic Centre, both using IceCube data. For the neutrino-line analysis, five years of IceCube data are considered to search for neutrinos from the annihilation and the decay of dark matter particles with masses between 10 GeV and 40 TeV. When considering the $\nu\bar{\nu}$ channel, this analysis provides the strongest limits on the thermally-averaged self-annihilation cross-section for masses below 1 TeV, as well as the leading lower limits in terms of dark matter decay lifetime from neutrino experiments. The second presented analysis is a low energy dark matter search using eight years of DeepCore data to probe dark matter masses ranging from 5 GeV to 1 TeV, for annihilation through $\nu_{e}\bar{\nu}_{e}$, $\nu_{\mu}\bar{\nu}_{\mu}$, $\nu_{\tau}\bar{\nu}_{\tau}$, $\mu^{+}\mu^{-}$, $\tau^{+}\tau^{-}$, $W^{+}W^{-}$ and $b\bar{b}$. When considering dark matter annihilation into $\tau^{+}\tau^{-}$, the sensitivities on the thermally-averaged dark matter self-annihilation cross-section achieved by this analysis demonstrate an improvement by an order of magnitude over previous searches with IceCube and other neutrino telescopes, with $\langle\sigma_{\mathrm{A}}\upsilon\rangle = 3.25\times10^{-24} \mathrm{cm}^3\mathrm{s}^{-1}$ at 10 GeV for the Navarro-Frenk-White halo profile.