No cost? Nope. It will all depend on your fare and rules applying to it.

You would have to go back to the place where you purchased your ticket and check there. If you haven't used any of it, then your entire ticket will be repriced to the new fare based on your new date.

It will most likely cost more plus the change / cancellation fee.

PS - you most likely heard wrongly about Emirates' no cost to changing your ticket too. All airlines adhere to their fare rules.