Can you please post a pic of the cage and litterbox? That would help immeasurable as we could see your set up and help suggest things!

Is he neutered?

The cage setup that seems to work best is to have the hay next to the litterbox so that he can eat and poop at the same time. The going outside of the box is a bit strange. Are you putting some pee-soaked paper pieces into his litterbox to see if he get the hint? How does he react when you pet him?

http://www.rabbit.org/faq/sections/litter.html#dribbling

take a look at the HRS FAQ… particularly 8.14 & on…

i would try changing the litterbox.  try an extra large high side corner box in the corner he usually goes and attach it to the bars so it cannot be shoved around.  i assume you put hay in the box?  keep doing that, and maybe try puting a bit of fresh herb in there to entice him in.  your rabbit is not a senior is he?  he can jump into the box… he just doesn’t use it, right? 

you’re going to need to pretty much start over from scratch.  he may be getting settled in your house and making himself king of the world.  if there are other pets around he may be trying to claim territory.  if he starts to show improvement, i would consider expanding his caged area if he’s only out for a couple hours a day… it’s nice for him to be able to run and play a bit even while you’re at work.  having nothing in his cage will make him extremely bored and depressed, i would put his toys back in, or like i said, attach an xpen so he can have his toys in there and move betw/ the two spaces.  if you attach the litterbox all he’ll be able to move is his food dish and toys, and that’s his right to do.

finally, when was the last time he’s seen a vet?  he may have an infection that needs to be addressed.

Ok, mine do the same thing with that type of litter pan, I’d suggest grabbing one of these

http://www.petsmart.com/product/index.jsp?productId=2752717&cp=2767038.2769319&fbn=Taxonomy%7CLitter+Training&fbc=1&clickid=topnav_dropdown6_link8&parentPage=family&keepsr=1

He doesn’t mean to pee outside of it, but rabbits back right up and raise their bum to pee; This litter box has a high back; It also has a grid so they can’t scatter the litter and it attaches to the cage:

This should solve the problem!

You might try a different brand of litter while you’re at it. There are several recommended on this forum.
I had to change to the plain white Carefresh when I had my allergies start up. He liked it better too.
Put the pee soaked bit in to get him started along with a few poops. And the hay as suggested above.

most importantly – he’s been neutered right? that can make a huge difference.
also – it may be that he’s peeing outside of his box due to a health issue. He doesn’t seem to be straining, not drinking or have white colored pee does he?

I’d also recommend switching litters and putting his box by the hay. I also like those high-back litterboxes, since they can help contain the mess.
If he really wants his box by his bowl, then I would recommend keeping in there, even if it seems difficult. It sounds like he’s decided it belong there and will continue going there.

you may also want to give his pen a good cleaning with vinegar / water mix since it helps remove the scent and staining.

Normally I would recommend adding another litterbox to encourage him to use the box – but his cage is fairly small.
that size cage is pretty small for a rabbit of his size, you might really consider building him an NIC condo, you can find out more about them in the cool habitats section of the site.