We have carried out quantum-mechanical calculations of the cubane C8H8, methylcubane C9H10 and various cubane-based oligomers with the original nonorthogonal tight-binding potential. The temperature dependence of cubane and methylcubane lifetimes to the decomposition moment was determined. The activation energies and frequency factors of the Arrhenius equation were found. Also, geometries and energetic properties of the cubane-based oligomers were calculated.