No, only mother has to file N-400. As long as the kid was in your and her custody, living with you, he will become a US citizen by operation of law. It's also beneficial to apply for certificate of naturalization for that kid once he becomes a US citizen. It costs over $1000, but it will ensure the kid will never have issues proving he is a citizen when applying for some jobs or renewing passport. He may be asked for proof 30 years later when you or your spouse may no longer be around.
Also, did your spouse have a conditional green card or always 10 year GC? If she still has a conditional green card, did she and her son apply for I-751?