Find Hypercube graph in graph with same size vertex set

Question

Let $G=(V,E)$ be a graph with $|V|=2^n$ for some $n\in\mathbb{N}$ and $\mathrm{deg}(v) \geq n$. Is there a way to check whether there exists a subset $E'\subset E$ such that $G'=(V,E')=C_n$, $C_n$ being the hypercube graph on $2^n$ vertices? I am completely lost on this one and looking for any input on how to approach this.