  The Euler-Heisenberg black holes with quantum electrodynamics (QED)
correction are embraced by a cavity in this paper, which serves as a boundary
of the black hole spacetime and contributes to the equilibrium of the system.
We explore the thermodynamic properties of the black hole, including the phase
transitions and phase structures. The small/large black hole phase transition
occurs for a negative QED parameter, while the reentrant phase transition can
be observed for a small positive QED parameter. Then the thermodynamic geometry
is investigated to diagnose microscopic interactions of black hole
thermodynamic systems. For the reentrant phase transition, the small black
holes are dominated by repulsion for the first-order coexistence curve, while
the interaction between the small black hole molecules could be attractive or
repulsive for the small/large black hole phase transition.
