6000mAh is the capacity, it means 6 amps for 1 hour which would also do 3 amps for 2 hours or 1 amp for 6 hours but NOT 360 amps for 1 minute, it's not really linear because you will likely get 1 amp for a little more than 6 hours and if you could get 360 amps for a second before it burst into smoke and possibly flames you would only get it for a quick second if at all.
For instance a good 3.7v Li IMR formulated cell may be rated 4200mAh and say 20a/50a which is 4.2a for 1 hour and it will put out 20a for a minute or so and 50a for a few seconds at a time which is what the ratings are all about, they are made mostly for the vape market so we benefit with a high drain capable cell.
However you should not plan to power a 20a load with this, that's a short burst rating, 4200mAh as a guild suggests around 4 amps as your max sustained load however it varies, it's best to use more battery than you need and they will last longer, that is cycle " charge and discharge " for a longer lifespan if not stressed to the max.
Something I look at is how much a battery sags under load, if it drops more than 10% under load I am not happy.
p.s. Your driver will draw the current/amps it needs, what you want is to make sure your battery voltage is within the drivers input range and that your battery is up to your task as explained above.
A bucking driver won't need as much battery capacity if you are putting in more voltage than you are getting out, remember volts x amps = watts so you need to look at the watts out and watts in because if you are using a boost driver that puts out a higher voltage than you put in you will need more battery capacity.
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What driver/laser do you have ?
If your driver is putting out 3a @ 5v and is a boost driver you will need a healthy battery as it will need to put out over 3a probably closer to 5a and you can't trust the Chinese ratings especially of the cheap cells, if it's a buck driver then any good pair of cells should do fine.
As too your original question a battery puts out voltage and the capacity is how much current is available as rated over time, you wont hurt it with too big of a battery as long as your voltage is correct/within spec, in short more mAh just means it will run longer.