We analyze VLBI delays back to 1984 from the permanent geodetic network, and ten superconducting gravimeter records from the Global Geodynamic Project spanning more than 7 years. From the former data, we deduce nutation o sets, and from the latter we get gravimetric factors. Comparison of these observed quantities against theoretical expressions of the core and mantle admittance to the tidal potential allows us to estimate Love numbers and resonant frequencies and quality factors of the core. We point out strengths and deficiencies of each technique in their ability to retrieve the Earth's interior parameters.