Let $Q_n$ be the $n$-dimensional hypercube graph (so that $Q_n$ has $2^n$ vertices and $n{2}^{n-1}$ edges). Is it true that, for every $ϵ>0$, if $n$ is sufficiently large, every subgraph of $Q_n$ with$$\ge ϵn{2}^{n-1}$$many edges contains a $C_6$?