JavaScript version of this could really use a "don't use eval() or similar" clause.

this.number = number? Is there some gain achieved by that?

Why create the additional variable i? There's nothing wrong with modifying the number parameter (which is a copy, and won't affect anything on the caller's side).

There's no reason to start i at 0; you can start it at 2. You can also put each if condition into one expression and take advantage of short-circuit evaluation. (I'm assuming the reason you used an else if is to avoid doing the extra check of an || expression because as soon as you know i % 3 === 0, there's no need to check the other case -- but that's how boolean expressions work anyway :))

You need to declare sum and i with var; as is, this spills them out as globals.