I hope you would consider the potential consequences of your sons standing up to the kid by fighting back; a "but, he did it first" excuse will not stop your kids from getting into trouble. From the sounds of it, that bully already has problems, he is not worth potentially getting your kids into trouble.
I think LT and Bob have the best suggestions: contact the child's parents and express your reluctant willingness to contact and involve other authorities if necessary.
You also mention that he has been bullying other children; if you know the names of those children then also get in contact with their parents and let them know what is going on. Encourage them to make the school aware of what is happening to their children.
If you find these efforts taking too long to produce results, perhaps in the short-term you can get more involved in school activities to keep an eye on your sons. Or, if possible doing simple things like going to pick them up after school to try and limit the time your sons can potentially run into the bully.
My little cousin was actually having bully problems not too long ago, and when he finally told his father, his father sought to get in contact with the other boy's parents and meet with them face-to-face. He remained calm - not threatening to sue, call the cops, retaliate or get revenge - rather choosing to let the parents know their son was doing these things and the extremely negative affect it had on his son (such as he, too, no longer wanted to go to school) and the worry it caused him because of how dearly he loved his son and all that he had sacrificed for him. Let the parents of the bully also know that you do not want their child to be branded a certain way and have to deal with potentially stiff consequences of his actions.
In the meantime, try to keep up the spirits of both your sons. I know this can be difficult (and I in no way mean to imply you are not already doing this). Things like cooking their favorite meals, giving them a bit more desert than normal, letting them stay up a half-hour or even an hour later, etc. can all brighten their spirits a little. Perhaps tie these things back to their school, making them seem like "rewards" for something positive they accomplished at school, or simply as a reward for telling you about how their school day went.
I hope this issue works out for you, and more importantly for your kids. No kid deserves to be put through something very tough like getting bullied.
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