chesskid.com you can find it in more, or just typing it in to your browser
Is there a kids section within chess.com?

Sure, this is also chess.com ( for kids though )
http://www.chesskid.com/?gclid=CKr6z-Wvn7wCFa47MgodtCsA0A

I just signed up my son for chess.com (he is 8). I wondering whether there is a kids section on chess.com because within the profile it doesn't even allow for birth years later than 2001. I also would prefer if he would not get bombarded with advertising and upgrade offers. Can anybody point me in the right direction?
For the first part of your question, yes, there's chesskid.com, as others have pointed out.
As for ads and upgrade offers... no, unfortunately he will keep on getting those unless he upgrades to a premium account. All free members get those all the time, and to some extent it's probably intended to be another reason for you to upgrade.
I just signed up my son for chess.com (he is 8). I wondering whether there is a kids section on chess.com because within the profile it doesn't even allow for birth years later than 2001. I also would prefer if he would not get bombarded with advertising and upgrade offers. Can anybody point me in the right direction?