  The (poset) cube Ramsey number $R(Q_n,Q_n)$ is defined as the least~$m$ such
that any 2-coloring of the $m$-dimensional cube $Q_m$ admits a monochromatic
copy of $Q_n$. The trivial lower bound $R(Q_n,Q_n)\ge 2n$ was improved by Cox
and Stolee, who showed $R(Q_n,Q_n)\ge 2n+1$ for $3\le n\le 8$ and $n\ge 13$
using a probabilistic existence proof. In this paper, we provide an explicit
construction that establishes $R(Q_n,Q_n)\ge 2n+1$ for all $n\ge 3$.
