It is assumed that heavy dark matter particles (HDMs) with the mass of O(TeV) are captured by the Sun. HDMs decay to relativistic lighter dark matter particles (LDMs). These high energy LDMs 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. With the different lifetimes of decay of HDMs and Z$^{prime}$ masses, the distributions and numbers of expected LDMs and neutrinos were evaluated at IceCube in the energy range between 1 TeV and 200 TeV in this work. To evaluate the capability of measurement of these LDMs from the sun core at IceCube, two observation results were assumed: one is the observation is consistent with the number of expect neutrinos; the other is no events are observed in this measurement. Based on these two assumptions, the upper limits for LDM fluxes were computed at 90% C.L.. With $m_{Z^{prime}} lesssim$ 400 GeV and $tau_{phi} lesssim 10^{23}$ s, finally, it is revealed that these LDMs could be measured in the energy range between O(1TeV) and O(100TeV) at IceCube.
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