Angular distributions for the inclusive He4 and He6 production cross sections in the He8+Pb208 system at incident energies of 16 and 22 MeV measured at the SPIRAL facility of the GANIL laboratory are presented. Using a combination of kinematical arguments and distorted wave Born approximation (DWBA) calculations, neutron transfer reactions were inferred to be the dominant contributors to both inclusive cross sections. Model-dependent values for the ratios of two- to one-neutron stripping, σ2n/σ1n, were derived and compared with previous results for He8 and He6 projectiles incident on other heavy targets. Three- and four-neutron stripping were inferred to be the main processes leading to He4 production, although the exact mechanism remains to be elucidated.