The default configuration of squid on a Debian/Ubuntu system is going to run as the user/group proxy/proxy
.
The simplist, and most likely explaination for your problem is that squid doesn't have write access to that folder with the privileges it has as the user proxy
.
Unless you have a really good reason, you should probably just leave the logging and cache to the default locations of /var/log/squid3/
and /var/spool/squid3/
which have the permissions setup properly.