Congrats on a new puppy!!!
First off, 6 weeks is kinda young, how come you got him so young?
He really needs his mom at this age, but anyway now you have him and he has successfully trained you to let him out at night huh. ;f
I would feed him as late as possible for your schedule, I am thinking like 10pm-midnight for his last feeding. Then outside for a bowel movement within about 20mins after eating. He should be able to sleep till 6am with this type of schedule.
DO NOT LET HIM OUT OF THE CAGE FOR whining, crying, barking etc. If its close to 6am make him get quiet first, then let him outside. Play time and potty time are 2 different things, don't confuse the 2 for him. Play time can also stimulate a B/M so be watchful of this.
Give him lots of stimuli (noises, cars, ball playing) during the day and wear his little butt out after the night time feeding and B/M. So that you will be able to sleep thru the night.
Do a web search for the "critical age of socialization" and start working on that stuff with him and good luck with the housebreaking.
Sounds like you are off to decent start so shouldn't take to long.
If you need more help post or pm me.
Did you pet your dog today?
Proud owner of Black rifles and Assault Canines !!!