We recorded absorption spectra of diborane(6), B2H6 and B2D6, dispersed in solid neon near 4 K in both mid-infrared and ultraviolet regions. For gaseous B2H6 from 105 to 300 nm, we report quantitative absolute cross sections; for solid B2H6 and for B2H6 dispersed in solid neon, we measured ultraviolet absorbance with relative intensities over a wide range. To assign the mid-infrared spectra to specific isotopic variants, we applied the abundance of B-11 and B-10 in natural proportions; we undertook quantum-chemical calculations of wavenumbers associated with anharmonic vibrational modes and the intensities of the harmonic vibrational modes. To aid an interpretation of the ultraviolet spectra, we calculated the energies of electronically excited singlet and triplet states and oscillator strengths for electronic transitions from the electronic ground state.