For ligand-protected gold clusters, geometrical differences of gold cores and/or the presence of secondary gold core-ligand interactions influence their unique optical and electronic properties and can, in principle, be detected by spectral changes of gold core vibrations (phonon modes) in ultralow-frequency Raman spectroscopy. We report experimental and theoretical Raman spectra of Au8 clusters protected by phosphine ligands particularly in the "gold cluster fingerprint" region from 50 to 150 cm-1 Raman shift (1.5 to 4.5 terahertz, THz). A characteristic core breathing mode observed at ca. 123 cm-1 was sensitive to differences of core geometries. A new band was found at ca. 150 cm-1, originating from a local strain on a polyhedral gold core caused by weak Au···π interactions. THz Raman spectroscopy can be utilized for metal nanoclusters to visualize core structural changes and Au···π interactions, which cannot be captured by single crystal X-ray analysis.