  Nonlinear electrodynamic (NLED) theories are well-motivated for their
extensions to classical electrodynamics in the strong field regime, and have
been extensively investigated in seeking for regular black hole solutions. In
this paper, we focus on two spherically symmetric and static black hole
solutions based on two types of NLED models: the Euler-Heisenberg NLED model
and the Bronnikov NLED model, and calculate the weak deflection angle of light
by these two black holes with the help of the Gauss-Bonnet theorem. We
investigate the effects of the one-loop corrections to quantum electrodynamics
on the deflection angle and analyse the behavior of the deflection angle by a
regular magnetically charged black hole. It is found that the weak deflection
angle of the electrically charged Einstein-Euler-Heisenberg black hole
increases with the one-loop corrections and the regular magnetically charged
black hole based on the Bronnikov NLED model has a smaller deflection angle
than the singular one. Besides, we also calculate the deflection angle of light
by the geodesic method for verification. In addition, we discuss the effects of
a cold non-magnetized plasma on the deflection angle and find that the
deflection angle increases with the plasma parameter.
