We present an extension of the c-axis tight-binding sum rule discussed by Chakravarty, Kee, and Abrahams [Phys. Rev. Lett. 82, 2366 (1999)] that applies to multilayer high-T-c cuprate superconductors (HTCS) and use it to estimate-from available infrared data-the change below T-c of the c-axis kinetic energy, <H-c>, in YBa2Cu3O7-delta (deltaapproximate to0.45,0.25,0.07), Bi2Sr2CaCu2O8, and Bi2Sr2Ca2Cu3O10. In all these compounds <H-c> decreases below T-c and except for Bi2Sr2CaCu2O8 the change of <H-c> is of the same order of magnitude as the condensation energy. This observation supports the hypothesis that in multilayer HTCS superconductivity is considerably amplified by the interlayer tunneling mechanism.