The lowest-energy structures and stabilities of the BLi(n)+ (n = 1-7) cluster cations are reported using the B3LYP, MP2, and CCSD(T) methods with the 6-311 + G(d) basis set. The first three-dimensional ground state in BLi(n)+ occurs for BLi5+ and the impurity, B atom, is seen to be trapped in an Li cage from BLi5+ onwards. Significant changes occur for BLi(n)+ (n = 2-4) when compared with their corresponding neutral clusters. However, there is very little change between the geometries of neutral and charged clusters for BLi6+ and BLi7+. The evolution of the binding energies, vertical and adiabatic electron affinities, and dissociation enthalpies with the size of BLi(n)+, show an especial stability for BLi6+ among BLi(n)+ cluster cations. The unique stability of the 8-valence electron BLi6+ can be understood from the cluster electronic shell model (CSM).