The edge set of \(K_n\) cannot be decomposed into edge-disjoint octagons (or \(8\)-cycles) when \(n \not\equiv 1 \pmod{16}\). We consider the problem of removing edges from the edge set of \(K_n\) so that the remaining graph can be decomposed into edge-disjoint octagons. This paper gives the solution of finding maximum packings of complete graphs with edge-disjoint octagons and the minimum leaves are given.