Yes, the question mark is necessary.
I found the following summary at Guide to Grammar and Writing.
There is some disagreement among writing reference manuals about when you should capitalize an independent clause following a colon. Most of the manuals advise that when you have more than one sentence in your explanation or when your sentence(s) is a formal quotation, a capital is a good idea. The NYPL Writer's Guide urges consistency within a document; the Chicago Manual of Style says you may begin an independent clause with a lowercase letter unless it's one of those two things (a quotation or more than one sentence). The APA Publication Manual is the most extreme: it advises us to always capitalize an independent clause following a colon.All the best.