We report ¹⁰⁵Pd nuclear magnetic resonance (NMR) and nuclear quadrupolar resonance (NQR) measurements on a single crystal of Ce₃Pd₂₀Si₆, where antiferroquadrupolar and antiferromagnetic orders develop at low temperature. From the analysis of NQR and NMR spectra, we have determined the electric field gradient (EFG) tensors and the anisotropic Knight shift (K) components for both inequivalent Pd sites—Pd(32f) and Pd(48h). The observed EFG values are in excellent agreement with our state-of-the-art density functional theory calculations. The principal values of the quadrupolar coupling are (20.37±0.02) MHz and (5.45±0.02) MHz, for the Pd(32f) and Pd(48h) sites, respectively, which is large compared to the Larmor frequency defined by the gyromagnetic constant γ=1.948 38 MHz/T for ¹⁰⁵Pd. Therefore, the complete knowledge of K and the EFG tensors is crucial to establish the correspondence between NMR spectra and crystallographic sites, which is needed for a complete analysis of the magnetic structure, static spin susceptibility, and the spin-lattice relaxation rate data and a better understanding of the groundstate of Ce₃Pd₂₀Si₆.