Identitical twins, Cole & Dylan Sprouse played Julian.  This could be either of them.

Alyson Hannigan at an event for Big Daddy (1999)

Joey Lauren Adams at an event for Big Daddy (1999)

Jessica Alba at an event for Big Daddy (1999)

Steven Bochco at an event for Big Daddy (1999)

Miko Blanco at an event for Big Daddy (1999)

Billy Connolly at an event for Big Daddy (1999)

Kim Delaney at an event for Big Daddy (1999)

Adam Sandler, Cole Sprouse, and Dylan Sprouse in Big Daddy (1999)

Cole Sprouse and Dylan Sprouse in Big Daddy (1999)