If $Q$, $E$, and $W$ denote respectively the heat added, change in internal energy, and the work done in a closed cycle process, then:

In a cyclic (closed cycle) process, the system returns to its initial state. Internal energy $E$ (or $U$) is a state function, meaning its value depends only on the state of the system, not the path taken.
$$\Delta E=E_{\text{final}}-E_{\text{initial}}$$
Since the final state is the same as the initial state, $\Delta E=0$.According to the First Law of Thermodynamics:
$$Q=\Delta E+W$$
For a cycle, $Q=0+W⟹Q=W$.