If your voicemail greeting is stating that your 'mailbox is full' after the greeting plays, then your inbox has reached its message limit: Standard GA Voicemail mailboxes are limited to a maximum of 30 voice and fax messages. (The Trash is excluded).
Messages that remain in your inbox for more than 14 days are automatically moved to your trash folder.
Messages in the trash folder will be permanently deleted after 30 days.
If you need to retain copies of your fax/voice messages, download the files to your computer hard-drive. It should then be removed from your GA Voicemail inbox to free up the message space.
Delete messages by marking the checkbox next the message you want to delete and then click the trashcan icon in the navigation bar. To quickly remove all message from your inbox click the check box in the navigation bar to select all, then click the trashcan icon.
Once the message count is below the message limit, The mailbox full message will no longer play to callers.