Your facial fat is going to go up and down with your bodyfat percentage. Whether one is a bodybuilder, boxer, cyclist, or whatever, you'll notice the difference in the face as one's body fat level changes. Sure, when you're younger, you're likely to have a softer-looking face. But you'll still see a difference if you do something to lower your bodyfat. Get your bodyfat (not necessarily your overall weight) down to where your abs become visible and I'm sure you'll see the difference in your face as well.
Adding to this, your face is typically the first place you lose body fat. Its stored there as non-essential fat and for whatever reason is typically burned/noticeable first.
The last place to lose fat is the lower abdominal region, which explains everyones obsession with losing it.
As other people have suggested, cutting carbohydrates or at least limiting them will pay off greatly towards losing fat. Its no secret that carbohydrates typically account for the majority of people's calories and is stored as fat.
Cardio, more specifically high intensity interval training (HIIT) and lifting will pay dividends towards losing body fat.