We show that the cubic compound PbBi2 is a topological semimetal hosting a sixfold band touching point in close proximity to the Fermi level. Using angle-resolved photoemission spectroscopy, we map the band structure of the system, which is in good agreement with results from density functional theory. Further, by employing a low energy effective Hamiltonian valid close to the crossing point, we study the effect of a magnetic field on the sixfold fermion. The latter splits into a total of twenty Weyl cones for a Zeeman field oriented in the diagonal, (111) direction. Our results mark cubic PbBi2 as an ideal candidate to study the transport properties of gapless topological systems beyond Dirac and Weyl semimetals.