The IceCube Neutrino Observatory is an optical Cherenkov detector instrumenting one cubic kilometer of ice at the South Pole. The Cherenkov photons emitted following a neutrino interaction are detected by digital optical modules deployed along vertical strings within the ice. The densely instrumented bottom central region of the IceCube detector, known as DeepCore, is optimized to detect GeV-scale atmospheric neutrinos. As upward-going atmospheric neutrinos pass through Earth, matter effects alter their oscillation probabilities due to coherent forward scattering with ambient electrons. These matter effects depend upon the energy of neutrinos and the density distribution of electrons they encounter during their propagation. Using simulated data at the IceCube Deepcore equivalent to its 9.3 years of observation, we demonstrate that atmospheric neutrinos can be used to probe the broad features of the Preliminary Reference Earth Model. In this contribution, we present the preliminary sensitivities for establishing the Earth matter effects, validating the non-homogeneous distribution of Earth's electron density, and measuring the mass of Earth. Further, we also show the DeepCore sensitivity to perform the correlated density measurement of different layers incorporating constraints on Earth's mass and moment of inertia.