Will 1ml of Juvederm (or another filler) have an effect on a young man's cheekbones?

Yes, you can improve the cheeks with 1 ml of filler, but it's difficult to determine how much filler you'll need without pictures and knowing your desired results. Both implants and fillers in the cheeks can create good results for patients. Both can build up the cheeks and create symmetry. You must balance the pros and cons of each procedure and do what you feel is the best decision for you.
Fillers:
Pros: No downtime Reversible Quick
Cons: Temporary More expensive in long run
Implants Pros: Permanent Great for patients with poor bone structure Less expensive overtime
Negative: Risks associated with surgery Possible infection Downtime
Hope this helps.

The answer to your question depends on the amount of imbalance and volume loss of your cheeks. Think of it this way, 1ml of filler is about 1/5th of a teaspoon. Therefore, areas like the cheeks often require multiple syringes of filler to achieve an optimal correction. In our practice, most patients use an average of 2 syringes of a filler such as Voluma or Lyft. Another option would be to use a collaged stimulator such as Sculptra which provides a more gradual, but longer lasting enhancement. Make sure you see an experienced physician injector for an in-person consultation and evaluation to determine which treatment options are best for you. Best wishes.

Thank you for your
question about fillers to your cheeks.  Although an in-person consultation would benefit you the most, in general, 1-2cc of a filler like Voluma can lead to a significant improvement in cheek appearance.  In general, the younger you are, the less filler you'll need for cheek augmentation.  This is because your skin turgor is greater when you're younger (i.e. your skin is tighter), and so your skin expansion will be greater and the volume enhancement will look greater after the fillers are injected into your cheek.  Be sure to seek a
consultation with a board certified plastic surgeon who addresses all
your concerns and discusses the surgery details including the risks and
benefits of the procedure, recovery time, and post-operative course. 
Also, be sure to see plenty of before-and-after pictures in real patients, and not
just computer-generated images, who have a similar cheek appearance to yours, and preferably at different time
frames (3 weeks out, 3 months out, etc) to more accurately predict your own outcome.  And lastly, I think the most important component of
the consultation is to establish a good connection with your plastic
surgeon.  If you don’t feel you have a
good connection with your plastic surgeon after your consultation, he/she may
not be the best surgeon for you.
For more information on fillers, please refer to the link below.
Good luck.Mark K Markarian, MD, MSPH
Harvard-trained Aesthetic Plastic Surgeon