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We report $^{105}$Pd NMR and NQR measurements on a single crystal ofCe$_3$Pd$_{20}$Si$_6$, where antiferroquadrupolar and antiferromagnetic ordersdevelop at low temperature. From the analysis of NQR and NMR spectra, we havedetermined the electric field gradient (EFG) tensors and the anisotropic Knightshift ($K$) components for both inequivalent Pd sites - Pd($32f$) andPd($48h$). The observed EFG values are in excellent agreement with ourstate-of-the-art DFT calculations. The principal values of the quadrupolarcoupling are $(20.37 \pm 0.02)$ MHz and $(5.45 \pm 0.02)$ MHz, for thePd($32f$) and Pd($48h$) site, respectively, which is large compared to theLarmor frequency defined by the gyromagnetic constant $\gamma = 1.94838$ MHz/Tfor $^{105}$Pd. Therefore, the complete knowledge of $K$ and the EFG tensors iscrucial to establish the correspondence between NMR spectra andcrystallographic sites, which is needed for a complete analysis of the magneticstructure, static spin susceptibility, and the spin-lattice relaxation ratedata and a better understanding of the groundstate of Ce$_3$Pd$_{20}$Si$_6$.

$^{105}$Pd NMR and NQR study of the cubic heavy fermion system Ce$_3$Pd$_{20}$Si$_6$