Since the discovery of metal-doped boron clusters attracted great significance to create a new class of materials, research interests have been directed to chemical bonding and structural evolution of lanthanide boride clusters. Here, we perform an extensive ground-state structure search for the CeBn and CeBn- clusters in the size range from 9 to 18 using the Crystal structure AnaLYsis by Particle Swarm Optimization method and density functional theory optimization. It is found that the ground-state structures in both neutral and anionic series possess half-sandwich geometry. The host boron moiety in neutral series has a tendency to form borophene-like geometry. The pentagonal and hexagonal holes are more common in the larger anionic CeBn- series. The theoretical photoelectron spectroscopy has been simulated by applying time-dependent density functional theory calculations. The neutral CeB14 cluster is identified as a magic cluster on the basis of its robust relative stability with respect to its neighbors. Electronic structure and chemical bonding analyses reveal that the CeB14 cluster possesses a large HOMO-LUMO gap and enhanced stability with strong delocalized π and δ bonding via interactions between the Ce 5d- and B 2p-AOs.