Double-and triple-walled carbon nanotubes are studied in detail by laser energy-dependent Raman spectroscopy in order to get a deeper understanding about the second-order G band Raman process, general nanotube properties, such as electronic and vibrational properties, and the growth method itself. In this work, the inner nanotubes from the double-and triple-walled carbon nanotubes are produced through the encapsulation of fullerene peapods with high-temperature thermal treatments. We find that the spectral features of the G band, such as the intensity, frequency, linewidth, and line shape are highly sensitive to the annealing temperature variations. We also discuss the triple-peak structure of the G band observed in an individual triple-walled carbon nanotube taken at several laser energies connecting its Raman spectra with that for the G band spectra obtained for bundled triple-walled carbon nanotubes.