The motion of a container filled with fluid perturbs the free surface and may result in spilling. In practice, most of the energy is localized in the modes of lowest frequencies (the gravest modes), and sloshing can be predicted once the dynamics of these modes is known. In this Rapid Communication, we investigate the nonlinear interactions between such grave modes in a cylindrical container. We first show that energy can be transferred from modes to modes with three-wave interactions: we derive the resonance conditions and characterize the early stage of this interaction. This result strongly contrasts with resonant interactions between surface gravity waves in extended domains such as the ocean, which involve at least four waves and are thus less efficient. An experiment is then performed to provide evidence of these nonlinear interactions.