The specific heat of high quality (LaB6)-B-N (N = 10, 11, natural) single crystals is investigated in a wide range of temperatures 2 similar to 300 K. The obtained data allow to estimate correctly (i) the electronic gamma. T term of specific heat (gamma approximate to 2.4 mJ/(mol.K-2)), (ii) the contribution from quasilocal vibrating mode of La3+ ions (Theta(E) approximate to 150 - 152 K), (iii) the Debye-type term from rigid boron cages (Theta(eta) approximate to 1160 +/- 40 K). Our data also suggest an additional defect-mode component (iv) which may be attributed to a contribution of 1.5% boron vacancies in LaB6. The obtained results may be interpreted in terms of formation of two level systems, which appear when La3+ ions are displaced from their centrosymmetric positions in the cavities of rigid boron cages, apart from randomly distributed boron vacancies in the LaB6 matrix.