Currently, there is no such report in Adaxes, but for the next version we are going to completely rework the Reports subsystem, which will allow you to create custom reports on your own. Starting from the next version, it will be possible to create mailbox size reports.
For now, you can achieve this using a PowerShell script. You can create a script that generates a report on the sizes of the mailboxes you need in an HTML or CSV format and saves the report to a certain file share or sends it by e-mail. Also, you can create a Custom Command or a Scheduled Task executing the script to be able to run the report on demand or on a certain schedule.
To help you with the scripts, have a look at the following samples:
If you need more assistance with the script, we will help you.