Raman measurements on high quality, relaxed InN nanocolumns grown on Si(001) and Si(111) substrates by plasma-assisted molecular beam epitaxy are reported. A coupled LO phonon-plasmon mode around 430 cm-1, together with the uncoupled LO phonon appears in the nanocolumnar samples. The coupled mode is attributed to spontaneous accumulation of electrons at the lateral surfaces of the nanocolumns, while the uncoupled phonon originates from their inner part. Infrared reflectance measurements confirm the presence of electrons in the nanocolumns. The electron density in the accumulation layer depends on the growth temperature and is sensitive to exposure of HCl. Our results indicate that accumulation of intrinsic electrons occurs not only at the polar surfaces of InN layers, but also on non-polar lateral surfaces of InN nanocolumns. Its origin is attributed to an In-rich surface reconstruction of the nanocolumns sidewalls.