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The cuprate high temperature superconductors exhibit a pronounced trend in which the superconducting transition temperature Tc increases with the number of CuO2 planes n in the crystal structure. We compare the magnetic excitation spectrum of Bi2+xSr2-xCuO6+δ (Bi-2201) and Bi2Sr2Ca2Cu3O10+δ (Bi-2223), with n=1 and 3, respectively, using Cu L3-edge resonant inelastic x-ray scattering. Near the antinodal zone boundary we find the paramagnon energy in Bi-2223 is substantially higher than that in Bi-2201, indicating that multilayer cuprates host stronger effective magnetic exchange interactions, providing a possible explanation for the Tc vs n scaling. In contrast, the nodal direction exhibits very strongly damped, almost nondispersive excitations. We argue that this implies that the magnetism in the doped cuprates is partially itinerant in nature. © 2014 American Physical Society.