We studied the compression and heating of cone-inserted spherical, solid CD shell and DT ice layer targets in strong external magnetic fields using the fast ignition integrated interconnecting simulation system (FI3). The simulation results show that the compression of these spherical targets is stable and that it has the potential to produce a high-areal-density core plasma. In a compressed plasma in an external magnetic field, the magnetic mirror ratio is less than four, which does not reflect the hot electrons needed for core heating. Magnetic beam guiding also significantly enhances the heating efficiency for both CD and DT ice targets.