Running follow SQL query either in Powershell or within SQL against multiple servers

I am running into a mental block and trying to figure how I would run the following query against mulitple SQL servers. I thought about declaring a list within my query and simply running the query command against the list (that didn't work out for me), someone mentioned Powershell. I am relatively new still to Powershell. If anyone has any ideas to help that would be great.

Thanks.

DECLARE @tableHTML  NVARCHAR(MAX) ;

SET @tableHTML =
    N'<H2>DB Backups</H2>' +
    N'<table border="0" style="font-family:Verdana;font-size:11px">' +
    N'<tr><th>Database Name</th>' +
    N'<th>Date</th>' +
    N'<th>Backup Location</th>' +
    N'<th>Server Name</th><th>Recovery Model</th><th>Backup Type</th>' +
    N'<th>Time Taken</th>' +
        CAST ( (
    SELECT TOP 10
     td = database_name,       '',
     td = backup_start_date, '',
     td = physical_device_name, '',
                    td = server_name, '',
                    td = recovery_model, '',
                    td = '' ,
                    CASE s.[type]
      WHEN 'D' THEN 'Full'
      WHEN 'I' THEN 'Differential'
      WHEN 'L' THEN 'Transaction Log'
     END AS BackupType,
     td = CAST(DATEDIFF(second, s.backup_start_date,s.backup_finish_date) AS VARCHAR(100)) + ' ' + 'Seconds'
              FROM msdb.dbo.backupset s
   INNER JOIN msdb.dbo.backupmediafamily m ON s.media_set_id = m.media_set_id
   ORDER BY backup_start_date DESC, backup_finish_date                                          
              FOR XML PATH('tr'), TYPE
    ) AS NVARCHAR(MAX) ) +
    N'</table>' ;

EXEC msdb.dbo.sp_send_dbmail
    @recipients='someone@home.com',
    @subject = 'DB Backups',
    @body = @tableHTML ,
    @body_format = 'HTML'