  We report $^{105}$Pd NMR and NQR measurements on a single crystal of
Ce$_3$Pd$_{20}$Si$_6$, 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 DFT calculations. The principal values of the quadrupolar
coupling are $(20.37 \pm 0.02)$ MHz and $(5.45 \pm 0.02)$ MHz, for the
Pd($32f$) and Pd($48h$) site, respectively, which is large compared to the
Larmor frequency defined by the gyromagnetic constant $\gamma = 1.94838$ MHz/T
for $^{105}$Pd. 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 Ce$_3$Pd$_{20}$Si$_6$.
