Particle in a box interacting with a strong magnetic field

For a particle interacting with magnetic field applied along the z-direction and confined to 3D cubic box of length L. How can one interpret the magnetic length(l) and how does it compare to confinement length(L) of the box?

We know the energy spectrum for a free electron interacting with a magnetic field looks like

$$epsilon(n,k_{z})= hbar omega_{c}(n+frac{1}{2}) + frac{hbar^{2} k_{z}^{2}}{2m} $$

where $n =0,1,2….$ ; $k_{z}in mathbb{Z}$ and $omega_{c}=frac{eB}{mc}$ is the cyclotron frequency. In this case we obtain the magnetic length to be $l = sqrt{frac{hbar}{eB}}$.

I have been trying to find a way to contrast this with the cases where particle is confined to :

(i) 3D box of dimensions say ${L}$.

(ii) A cylinder of certain radius say $r_{0}$ and height $2 z_{0}$.