We present an analysis of the energetics and particle content of the lobes of 24 radio galaxies at the cores of cooling clusters. The radio lobes in these systems have created visible cavities in the surrounding hot, X-ray- emitting gas, which allow direct measurement of the mechanical jet power of radio sources over six decades of radio luminosity, independently of the radio properties themselves. We find that jet (cavity) power increases with radio synchrotron power approximately as image, where image depending on the bandpass of measurement and state of the source. However, the scatter about these relations caused by variations in radiative efficiency spans more than 4 orders of magnitude. A number of factors contribute to this scatter, including aging, entrainment, variations in magnetic field strengths, and the partitioning of energy between electrons and nonradiating heavy particles. After accounting for variations in synchrotron break frequency (age), the scatter is reduced by sim50%, yielding the most accurate scaling relation available between the lobe radio power and the jet (cavity) power. Furthermore, we place limits on the magnetic field strengths and particle content of the radio lobes using a variety of X-ray constraints. We find that the lobe magnetic field strengths vary between a few to several tens of microgauss depending on the age and dynamical state of the lobes. If the cavities are maintained in pressure balance with their surroundings and are supported by internal fields and particles in equipartition, the ratio of energy in electrons to heavy particles (k) must vary widely from approximately unity to 4000, consistent with heavy (hadronic) jets.