We determined the geometries and chemical bonding phenomena of the B₂₇ system in its dicationic, cationic, neutral, anionic and dianionic states using DFT computations. In both cationic and neutral states, the triple ring tubular forms correspond to the lowest-energy isomers, especially in B₂₇⁺. The cation B₂₇⁺ represents the first stable hollow cylinder having a triple ring among the pure boron clusters. In the anionic and dianionic states, the quasi-planar structures are favoured due to a charge effect. In the triple ring tube B₂₇⁺, strong diatropic responses to external magnetic field occur in both radial and tangential types of electrons, and thus confer it a characteristic tubular aromaticity. The presence of a consistent aromatic character contributes to its high thermodynamic stability. The shapes of calculated MOs of B₂₇⁺ TR can be predicted by the eigenstates of a simple model of a particle on a hollow cylinder. The number of electrons in a hollow cylinder should attain a number of (4N + 2M) with M = 0 and 1 for both radial and tangential electrons, depending on the number of non-degenerate MOs occupied, in order to properly fulfill the closed electron shells. In the case of B₂₇⁺, M = 0 for radial electrons and M = 1 for tangential electrons.