Magnetic susceptibility results for single crystals of the new cubic compounds UT$_2$Al$_{20}$ (T=Mn, V, and Mo) are reported. Magnetization, specific heat, resistivity, and neutron diffraction results for a single crystal and neutron diffraction and inelastic spectra for a powder sample are reported for UMn$_2$Al$_{20}$. For T = V and Mo, temperature independent Pauli paramagnetism is observed. For UMn$_2$Al$_{20}$, a ferromagnetic transition is observed in the magnetic susceptibility at $T_c$ = 20 K. The specific heat anomaly at $T_c$ is very weak while no anomaly in the resistivity is seen at $T_c$. We discuss two possible origins for this behavior of UMn$_2$Al$_{20}$: moderately small moment itinerant ferromagnetism, or induced local moment ferromagnetism.