  Consider a charged Bose gas without self-interactions, confined in a three
dimensional cubic box of side $L\geq 1$ and subjected to a constant magnetic
field $B\neq 0$. If the bulk density of particles $\rho$ and the temperature
$T$ are fixed, then define the canonical magnetization as the partial
derivative with respect to $B$ of the reduced free energy. Our main result is
that it admits thermodynamic limit for all strictly positive $\rho$, $T$ and
$B$. It is also proven that the canonical and grand canonical magnetizations
(the last one at fixed average density) are equal up to the surface order
corrections.
