While you can’t forge Skyforge Steel, if you have completed the Companion’s questline, you are able to craft Ancient Nordic Armor and Nord Hero weapons instead.
However, after joining the Companions, you are able to buy Skyforge Steel weapons from him at any time and he is the only merchant in the game where they can be found. While the Skyforge allows Eorland to craft Skyforge Steel weapons, which have the same design as regular Steel weapons but have the same base damage as Elven weapons, you can’t forge this particular weapon variety yourself. Located in Whiterun behind Jorvaskyrr, the Skyforge, run by Eorland Greymane, is one of two forges in the city, with the other, Warmaiden’s, under the ownership of Adrianne Avenicci.