  Listing copies of small subgraphs (such as triangles, $4$-cycles, small
cliques) in the input graph is an important and well-studied problem in
algorithmic graph theory. In this paper, we give a simple algorithm that lists
$t$ (non-induced) $6$-cycles in an $n$-node undirected graph in $\tilde
O(n^2+t)$ time. This nearly matches the fastest known algorithm for detecting a
$6$-cycle in $O(n^2)$ time by Yuster and Zwick (1997). Previously, a folklore
$O(n^2+t)$-time algorithm was known for the task of listing $4$-cycles.
