We systematically study the equilibrium geometries and electronic and magnetic properties of Gen+1 and VGen (n = 1-19) clusters using the density functional theory approach within the generalized gradient approximation. Endohedral structures in which the vanadium atom is encapsulated inside a Ge-n cage are predicted to be favored for n >= 10. The dopant V atom in the Ge-n clusters has not an immediate effect on the stability of small germanium clusters (n < 6), but it largely contributes to strengthen the stability for n >= 7. Our study enhances the large stability of the VGe14 cluster, which presents an Oh symmetry cagelike geometry and a peculiar electronic structure in which the valence electrons of V and Ge atoms are delocalized and exhibit a shell structure associated with the quasi-spherical geometry. Consequently, this cluster is proposed to be a good candidate to be used as the building blocks for developing new materials. The cluster size dependence of the stability, the vertical ionization potentials, and electron affinities of Gen+1, and VGen are presented. Magnetic properties and the partial density of states of the most stable VGen clusters are also discussed.