Transition metal-doped electronic deficiency boron clusters have led to a vast variety of electronic bonding properties in chemistry and materials science. We have determined the ground state structures of PdBn0/- (n = 10-20) clusters by performing CALYPSO search and density functional theory (DFT) optimization. The identified lowest energy structures for both neutral and anionic Pd-doped boron clusters follow the structure evolution from two dimensional (2D) planar configurations to 3D distorted Pd-centered drum-like or tubular structures. Photoelectron spectra are simulated by time-dependent DFT theoretical calculations, which is a powerful method to validate our obtained ground-state structures. More interestingly, two "magic" number clusters, PdB12 and PdB16, are found with enhanced stability in the middle size regime studied. Subsequently, molecular orbital and adaptive natural density partitioning analyses reveal that the high stability of the PdB16 cluster originates from doubly sigma pi aromatic and bonding interactions of d-type atomic orbitals of the Pd atom with tubular B-16 units. The tubular C-8v PdB16 cluster, with robust relative stability, is an ideal embryo for forming finite and infinite nanotube nanomaterials.