Over the 11-year solar cycle, small changes in the total solar irradiance (TSI) give rise to small variations in the global energy budget. It was suggested, however, that different mechanisms could amplify solar activity variations to give large climatic effects, a possibility which is still a subject of debate. With this in mind, we use the oceans as a calorimeter to measure the radiative forcing variations associated with the solar cycle. This is achieved through the study of three independent records, the net heat flux into the oceans over 5 decades, the sea-level change rate based on tide gauge records over the 20th century, and the sea-surface temperature variations. Each of the records can be used to consistently derive the same oceanic heat flux. We find that the total radiative forcing associated with solar cycles variations is about 5 to 7 times larger than just those associated with the TSI variations, thus implying the necessary existence of an amplification mechanism, although without pointing to which one.