I have never kept a shark, so hopefully others will chime in. I do know that they are typically kept in long, ideally racetrack shaped tanks without corners. With how large yours already is, I do not think a 60 cube is large enough. I assume the footprint is 24"x24".
Unfortunately, I would be looking to rehome it sooner than later. You already have at least 3 fish in that tank that will outgrow it (or already have). Generally, you want to avoid keeping Tangs and Angels (and Puffers & Triggers) with fish like Lionfish and Sharks. Likely the only way the shark will have a chance is if you rehome it to another, larger tank with suitable tankmates.
My advice is to get a bigger tank first, then add these larger fish. Don't buy fish that you can't house to maturity. And please don't add the shark to your 100 gallon tank with the Undulated Trigger, if you still have that.