In the present paper, it is assumed that there exist two species of dark matter: a heavy dark matter particle (HDM) with the mass of O(TeV) which is generated in early universe and a lighter dark matter particle (LDM) which is a relativistic product due to the decay of HDM. HDMs, captured by the earth, decay to high energy LDMs, and these particles can be measured by km$^3$ neutrino telescopes, like the IceCube detector. A $Z^{prime}$ portal dark matter model is taken for LDMs to interact with nuclei via a neutral current interaction mediated by a heavy gauge boson $Z^{prime}$. With the different lifetimes of decay of HDMs and Z$^{prime}$ masses, the event rates of LDMs, measured by IceCube, are evaluated in the energy range between 1 TeV and 100 TeV. According to the IceCube data, the upper limit for LDM fluxes is estimated at 90% C.L. at IceCube. Finally, it is proved that LDMs could be directly detected in the energy range betwen O(1TeV) and O(10TeV) at IceCube with $m_{Z^{prime}} lesssim 500 GeV$ and $tau_{phi} lesssim 10^{21}$ s.
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