from: https://technet.microsoft.com/en-us/library/jj863434(v=exchg.150).aspx
As previously stated, when you delete a mailbox, both the Exchange attributes and the Active Directory user account are deleted. The mailbox (and the archive mailbox, if it’s enabled) will be permanently deleted from the mailbox database after the mailbox retention period expires.
The following procedure shows how to delete a user mailbox. Use the same procedure to delete other mailbox types after navigating to the appropriate page in the EAC.
The mailbox is removed from the mailbox list.
Open the Exchange Management Shell as Administrator and execute the Remove-Mailbox cmdlet:
Remove-Mailbox "IpswitchAnalytics"