There have been previous threads on the board re this family. The man's name is Rouke, sometimes written as Roke or Rooke.
This is from the previous thread: Ann erroneously listed as being b End when she was b Lonan, Isle of Man
1841 census at Primrose Hill, Liverpool 556 21/22 pg 36
John ROOKE 42 ShoeM I
Ann ROOKE 45 N
James ROOKE 15 Y
Thomas ROOKE 12 Y
Joseph ROOKE 8 Y
Margaret ROOKE 6 Y

1851 census at 2 Webster Street, Liverpool 2179 694 pg 37 #146
John ROURKE, Head mar 53 Cordwainer, b Ireland
Ann ROURKE, Wife Mar 58, b Lancaster Lpool
Jas ROURKE, Son U 26 Cordwainer, b Lancaster Lpool
Josh ROURKE, Son U 19 Cordwainer, b Lancaster Lpool
Margt ROURKE, Daur U 16 At Home, b Lancaster Lpool

1861 census at 2 Webster Street, Liverpool 2665 54 pg 46 #237
John ROURKE, Head Mar 67 Shoe Maker, b Ireland
Ann ROURKE, Wife Mar 70, b Isle of Man

Check the archives of this board. I have more I copied. Donna