We present a quantitative analysis of two radio source samples having opposite extremes of ambient gas density that leads to important new conclusions about the magnetic energy in the intergalactic medium (IGM). We analyze here (1) a new, large sample of well-imaged "giant" extragalactic radio sources that are found in rarefied IGM environments and (2) at the other extreme, radio galaxies situated in the densest known IGM environments, within 150 kpc of rich cluster cores. We find that sources in the former sample contain magnetic energies E_B ~ 10⁶⁰-10⁶¹ ergs and could be viewed as important "calorimeters" of the minimum energy a black hole (BH) accretion disk system injects into the IGM. In contrast to the radiation energy released by BH accretion, most of the magnetic energy is "trapped" initially in a volume, up to ~10⁷³ cm³, around the host galaxy. But since these large, megaparsec-scale radio lobes are still overpressured after the active galactic nucleus phase (AGN), their subsequent expansion and diffusion will magnetize a large fraction of the entire IGM. This suggests that the energy stored in intergalactic magnetic fields will have a major, as yet underestimated effect on the evolution of subsequently forming galaxies. Comparison with the second, cluster core-embedded sample shows that the minimum magnetic energy E_B can be a strongly variable fraction of the inferred accretion energy E_acc, and that it depends on the ambient IGM environment. Cluster embedded AGNs inject significant energy as PdV work on the thermal ICM gas, and their magnetic energy, even ignoring the contribution from stellar and starburst outflows, is sufficient to account for that recently found beyond the inner cores of galaxy clusters. We discuss the various energy loss processes as these magnetized CR clouds (lobes) undergo their enormous expansion into the IGM. We conclude that the aggregate IGM magnetic energy derived purely from galactic black holes since the first epoch of significant galaxy BH formation is sufficiently large that it will have an important influence on the process of both galaxy and visible structure formation on scales up to ~1 Mpc.