Optimized geometries of cubic TiyOz and LixTiyOz were calculated using DFT cluster approach for clusters containing up to 23 atoms. The calculated geometries were compared with actual crystal structures observed on cubic TiO2 and Li-Ti-O spinel nanocrystals prepared by solvothermal synthesis. While the DFT approach reproduces satisfactorily the main structural characteristics of TiyOz clusters, in the case of LixTiyOz clusters the agreement between calculated and real structures is less satisfactory due to the small cluster size. Raman spectra calculated under harmonic approximation from the optimized geometries reproduce all important features of the experimental Raman spectra. The agreement of DFT calculated and experimental Raman spectra improves with increasing size of the cluster.