$ sudo chown -R apache:apache /vagrant/cake
If this doesn't work, add this line as it is in Vagrantfile:
config.vm.synced_folder "./", "/vagrant", owner: 'vagrant', group: 'apache', mount_options: ['dmode=777', 'fmode=777']
And "vagrant reload".
If even that didn't work, it might be because of SE linux. Turn off SE linux this way:
$ sudo getenforce
Enforcing
$ sudo setenforce 0
$ sudo getenforce
Permissive
Enforcing
$ sudo setenforce 0
$ sudo getenforce
Permissive
And "vagrant reload".