If you choose to case, sterilization is overkill and is generally viewed as a bad idea.
I used to bake my casing, let it cool, then case, etc., etc., but it really just adds another vector of contamination IME - casing layers develop cobweb and all kinds of nasties quite easily, whereas uncased grows perform about the same and are more resilient.
Your mileage may vary. Do what I did - try two tubs, one cased, one not and see what happens. That's when I stopped using a casing layer.
That said, your style & time constraints may differ from others. Cased cubes require more air exchange in my experience, while uncased tubs do great with simple poly-filled holes and a daily fanning / visual check (because you're gonna look).
In short, don't sterilize if you're gonna case - a sterile grow media is ripe for contams while a pasteurized one is more resistant.