The probable answer is that the cron job executes under your user - and the directory is owned by apache (or www-data or nobody or whatever user your web server runs as).
To get it to work, you could set up the cron job to run as the web server user.
Something like this:
su -l www-data -c 'crontab -e'
Alternatively, you could change the permissions to 775 (read-write-execute for the owner and group, and read-execute for others) and set the group ownership of the folder to the user running the cron job.
However, you have to make sure that if you're deleting something or descending into folder which is created by apache, you could still run into problems (apache would create a file which it itself owns, and your user cannot delete it then, regardless of the directory permissions.
You could also look at some stuff like suphp or whatever is up to date - where the web server processes are ran under your username, depending on your system architecture.
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