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.