Well it started off as our burning patch of the garden so the soil was already exposed.But other than that yep all by himself,he has dug out the hole patch before,one spot was 2ft deep. I never found our what he was looking for.

He also found an underground mouse nest(i think) in the middle of a stubble field,me and my friend,who had her springer, thought he had found treasure! I was amazed how he could find one little hole out of a whole 7 acre field!

I do hide things in the garden for him. I hide his breakfast and some extra nice treats every now and then. I also hide his kong sometimes too and i will hide some of his toys too.
And he loves it!
But now his attention has been stolen by the worms

Get the loppers on that mess of branches and bag it up and give him his digging patch back!

You could hire him out to those people who have those worm charming competitions!

http://www.blackwater-valley.org.uk/worm_charming.htm

If he digs your garden up he is neither physically nor mentally tired or satisfied. Beagles have a lot of energy and it seems that your current lifestyle does not enable him to expend it all every day.

Get on your bike and give him a good run and then see if he still wants to dig.