The structures and stabilities of square–hexagon alternant boron nitrides (B _x N _x , x=12–36) vs their tube isomers containing octagons, decagons and dodecagons have been computed at the B3LYP density functional level of theory with the correlation-consistent cc-pVDZ basis set of Dunning. It is found that octagonal B₂₀N₂₀ and B₂₄N₂₄ tube structures are more stable than their square–hexagon alternants by 18.6 and 2.4 kcal mol⁻¹, respectively, while the square–hexagon alternants of other cages are more stable. Trends in stability as a function of cluster size are discussed.