Oscillations with a periodicity around 6 years have long been observed in the Earth's rotation, expressed as changes in the length of day, and robustly attributed to dynamical processes in the fluid outer core pursuant to the analysis of geomagnetic data. Recently, a 6-year cycle has also been discovered in the global mean sea level changes and in some of its main contributors (i.e., mass balances of the ice sheets and glaciers). Here, we report additional observations of the 6-year cycle in the climate system. Large oscillations at periods around 6 years are detected in terrestrial water storage changes estimated from satellite gravity measurements and global hydrological models, in agreement with satellite and in-situ precipitation observations. We also find a significant 6year cycle in the global mean Earth's surface temperature observed since the beginning of the 1980s. Finally, in agreement with previous studies, we report a 6-year cycle in the atmospheric angular momentum in opposition of phase with the length of day. As changes in the length of day are in opposition with respect to changes in the solid Earth's rotation, this suggests that the atmosphere and the solid Earth rotate together at a 6-year period, possibly in response to deep Earth's processes. These new discoveries raise the question of the links between dynamical processes occurring in the core, solid Earth and superficial fluid envelopes at the 6-year period, as well as the nature of the mechanisms driving 6-year oscillations in integrative geodetic variables, such as the length of day or gravity field.