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In this paper, we presented the ground state energies calculated for somesingle and double cascade hyperon(${\Xi}^{-}$) hypernuclei. For hypernuclei ofthe type $_{\Xi}^{A_c+1}$X we applied $\Xi+^A_c$X two-body model and forhypernuclei of the type $_{\Xi\Xi}^{A_c+2}$X we adopted $\Xi+\Xi+^A_c$Xthree-body model. A two-term Gaussian (Isle type) potential with adjustableparameters is chosen as the $\Xi$-nucleus interaction, while a two-termYukawa-type potential has been chosen for the $\Xi\Xi$ pair. In the three-bodymodel calculation, we adopted the hyperspherical harmonics expansion (HHE)formalism. The resulting two- and three-body Schr{\"o}dinger equations subjectto appropriate boundary condition's have been solved numerically to get theground-state energies and wavefunctions. Computed values are in excellentagreement with the observed ones as found in the literature. Analysis of thecalculated observables indicates that the hyperons stay close to thecore-nucleus. Hypernuclei formed as a result of absorption of one or more$\Xi$-hyperon(s) by a normal nucleus (bound or unbound) are found to have morestability than those formed as a result of absorption of one or more $\Lambda$hyperon(s) by the same nucleus. This fact flashes towards the possibility ofthe existence of a valley of strange hypernuclei near the drip lines.

Hyperspherical few-body model calculation for cascade $\Xi$ exotic hypernuclei with reference to nuclear drip lines