Gunslick foam. There is another one, I am not home to look at my stuff to get the name right, I may post back up when I get it. The Gunslick foam works wonders. I took me about 4 attempts at what I thought was a clean rifle to get to cold steel. After that initial cleaning and ever since, I fill the barrel and 20 minutes later swab out the barrel and in maybe three patches, nothing but white cotton. I have not used a brush in two years except on my muzzleloader, which I clean the old fashioned way.
Downsides exist. The foam is murder on finishes and it melts certain kinds of plastics. Remove the barrle/action from the stock. Do NOT go berserk with the foam, having it spray out the barrel like snow is a very bad thing but you must fill the barrel, so there is some learning to do. It will absolutely postively eat a hole in carpet and blue jeans. You absolutely positively must wear safety goggles.
The other foam is not so poisonous but it also takes two times to get cold steel.
It runs about 10 bucks, mine has lasted two years. Its in a blue and silver/black can. Do not lose the filler hose. Follow the instructions to the letter, you will not be disappointed.
I should elaborate on the first time you use the foam. I position the barrel as level as I can get it, stick the filler tube in the throat, push the button with one hand and with my other hand i have a finger loosley over the muzzle. WHen I feel the foam, I relase the button, remove the filler, wipe everything clean with paper towels, and dispose of them in a metal #10 can. I used a brush when the first attempt to clean the barrel was not successful. The brush came apart and after using regular tools to get that mess cleaned up, I went back to the foam. I had multiple layers of carbon and copper to remove. If you leave the barrel in a muzzle down position you can watch black ooze drip out but understand that means the fluid is not cleaning since it ain't in the barrel. Until I got the barrel clean (it was my 300 Browning WInMag) I would run dry patches through and when they came out dry but dirty, I shot another round of foam down the barrel. Once a patch comes out dry and clean, a very light coat of your favorite oil may be recommended. Myself, I stick the barrel full of cotton balls.
Have fun and report back