The small numbers "310/35" you see imprinted at the base of the CISA lock are key identification numbers.
Get a pin and try to dislodge the broken key without pushing it further into the barrel. Then get some very fine needle nose pliers and pull it out.
Then you can contact the manufacturer for a 310/35 key and provide them will all the details of ownership, they should send you a key in a few days.
That's the padlock model number. Looks more like 810/65 to me too.
Best thing todo is try and remove the key.
Failing that the brass bolt padlock is through will be easier to cut than the padlock itself.
Drilling the lock it self is an option, however the barrel itself isn't always straight forward and are designed to resist it.
Looking at some pics of open CISA locks of same design, they secure both sides of the bolt, so drilling the lock barrel might be in effective anyway.
There are a few forums around that deal with lock picking, might be an idea to ask around on there, they often have locks that have been cut away to see the internals, would give a better idea of best place to drill.
Edit:
The original CISA 80 LOGO Line padlock with proven quality and security. 5 lever brass alloy mechanism is encased in 3mm stainless steel shell. The 12mm dia. hardened shackle rotates to make virtually saw and crop proof and the key entry is designed to break drill tips to again virtually make it drill proof.
I'd cut here:

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