Given a non-decreasing sequence S = (s 1 , s 2 , . . . , s k ) of positive integers, an Spacking edge-coloring of a graph G is a partition of the edge set of G into k subsets {X 1 , X 2 , . . . , X k } such that for each 1 ≤ i ≤ k, the distance between two distinct edges e, e ′ ∈ X i is at least s i + 1. This paper studies S-packing edgecolorings of cubic graphs. Among other results, we prove that cubic graphs having a 2-factor are (1, 1, 1, 3, 3)-packing edge-colorable, (1, 1, 1, 4, 4, 4, 4, 4)-packing edgecolorable and (1, 1, 2, 2, 2, 2, 2)-packing edge-colorable. We determine sharper results for cubic graphs of bounded oddness and 3-edge-colorable cubic graphs and we propose many open problems.