The cuprate high temperature superconductors exhibit a pronounced trend in which the superconducting transition temperature T sub(c) increases with the number of CuO sub(2) planes n in the crystal structure. We compare the magnetic excitation spectrum of Bi sub(2+x)Sr sub(2-x)CuO sub(6+ delta ) (Bi-2201) and Bi sub(2)Sr sub(2)Ca sub(2)Cu sub(3)O sub(10+ delta ) (Bi-2223), with n = 1 and 3, respectively, using Cu L sub(3)-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 T sub(c) 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.