Using a suite of radiation hydrodynamic simulations of star cluster formation in turbulent clouds, we study the escape fraction of ionizing (Lyman continuum) and non-ionizing (FUV) radiation for a wide range of cloud masses and sizes. The escape fraction increases as H II regions evolve and reaches unity within a few dynamical times. The cumulative escape fraction before the onset of the first supernova explosion is in the range 0.05-0.58; this is lower for higher initial cloud surface density, and higher for less massive and more compact clouds due to rapid destruction. Once H II regions break out of their local environment, both ionizing and non-ionizing photons escape from clouds through fully ionized, low-density sightlines. Consequently, dust becomes the dominant absorber of ionizing radiation at late times and the escape fraction of non-ionizing radiation is only slightly larger than that of ionizing radiation. The escape fraction is determined primarily by the mean $langle taurangle$ and width $sigma$ of the optical-depth distribution in the large-scale cloud, increasing for smaller $langle taurangle$ and/or larger $sigma$. The escape fraction exceeds (sometimes by three orders of magnitude) the naive estimate $e^{-langle taurangle}$ due to non-zero $sigma$ induced by turbulence. We present two simple methods to estimate, within $sim20%$, the escape fraction of non-ionizing radiation using the observed dust optical depth in clouds projected on the plane of sky. We discuss implications of our results for observations, including inference of star formation rates in individual molecular clouds, and accounting for diffuse ionized gas on galactic scales.
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