Connect:

$LiveCred = Get-Credential
$Session = New-PSSession -ConfigurationName Microsoft.Exchange -ConnectionUri https://ps.outlook.com/powershell/ -Credential $LiveCred -Authentication Basic –AllowRedirection
Import-PSSession $Session

Get-Mailbox | Get-MailboxStatistics | ft displayname, totalitemsize

$UserMailboxStats = Get-Mailbox -RecipientTypeDetails UserMailbox -ResultSize Unlimited | Get-MailboxStatistics
$UserMailboxStats | Add-Member -MemberType ScriptProperty -Name TotalItemSizeInBytes -Value {$this.TotalItemSize -replace "(.*\()|,| [a-z]*\)", ""}
$UserMailboxStats | Select-Object DisplayName,@{Name="TotalItemSize (GB)"; Expression={[math]::Round($_.TotalItemSizeInBytes/1GB,2)}}

$UserMailboxStats = Get-Mailbox -RecipientTypeDetails UserMailbox -ResultSize Unlimited | Get-MailboxStatistics
$UserMailboxStats | Add-Member -MemberType ScriptProperty -Name TotalItemSizeInBytes -Value {$this.TotalItemSize -replace "(.*\()|,| [a-z]*\)", ""}
$UserMailboxStats | Select-Object DisplayName,@{Name="TotalItemSize (GB)"; Expression={[math]::Round($_.TotalItemSizeInBytes/1GB,2)}} | Export-CSV "All-Mailboxes.csv" -NoTypeInformation

Remove-PSSession $Session