We present new Spitzer IRS spectroscopy of Cygnus A, one of the most luminous radio sources in the local universe. Data on the inner 20 are combined with new reductions of MIPS and IRAC photometry as well as data from the literature to form a radio through mid-infrared spectral energy distribution (SED). This SED is then modeled as a combination of torus reprocessed active galactic nucleus (AGN) radiation, dust enshrouded starburst, and a synchrotron jet. This combination of physically motivated components successfully reproduces the observed emission over almost 5 dex in frequency. The bolometric AGN luminosity is found to be 10^12 L_odot (90% of LIR), with a clumpy AGN-heated dust medium extending to sim130 pc from the supermassive black hole. Evidence is seen for a break or cutoff in the core synchrotron emission. The associated population of relativistic electrons could in principle be responsible for some of the observed X-ray emission though the synchrotron self-Compton mechanism. The SED requires a cool dust component, consistent with dust-reprocessed radiation from ongoing star formation. Star formation contributes at least 6 times 10^10 L_odot to the bolometric output of Cygnus A, corresponding to a star formation rate of sim10 M_odot yr-1.
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