The shadowing effect of the Moon and Sun in TeV cosmic rays has been measured with high statistical significance by several experiments. Unlike particles from directions close to the Moon, however, charged particles passing by the neighborhood of the Sun are affected not only by the geomagnetic but also by the solar near- and interplanetary-magnetic field. Since the latter undergoes a well-known 11-year cycle - during which it can become highly disordered - the cosmic-ray shadow cast by the Sun as observed on Earth is expected to change over time. We present an update of the analysis of the cosmic-ray Moon and Sun shadows using data taken with the IceCube Neutrino Observatory. With a median energy after quality cuts of approximately $50-60\, \mathrm{TeV}$, depending on the cosmic-ray flux model used, primary cosmic rays inducing events which pass IceCube's Sun shadow filter have a comparatively high energy. While the results for the Moon shadow confirm the stability of the IceCube observatory, the results for the Sun shadow exhibit a clear variation correlating with solar activity and theoretical models of the solar magnetic field.