Mit Filter:

$a = Get-MailboxDatabase
foreach ($b in $a)
{
  if ($b.Name -like "DB-Via-Premium*")
  {
    $b.Name + ": " + (Get-MailboxStatistics -Database $b.Name).Count
  }
}

Ohne Filter:

$a = Get-MailboxDatabase
foreach ($b in $a)
{
  $b.Name + ": " + (Get-MailboxStatistics -Database $b.Name).Count
}