2003 Toyota Camry Bolts in the engine block.

Yes, extracting the broken bolt(s) from the block is the cheapest route. Depending on the exact way it broke, here are a few tips of trying to remove the broken bolt(s).

Partial Bolt Above Surface

If a portion of the broken bolt remains accessible above the surface, there are several options for removing it. A stud puller, a pneumatic tool used in auto shops, may be able to extract the bolt remnant. A trip to your local auto shop and a small fee may resolve your problem. For a do-it-yourself attempt, you can drip hot melted paraffin wax around the bolt remnant threads, allowing it to wick down around the submerged bolt remnant. Once cool, apply a second coating of hot wax, another tablespoon or so, and allow it to set overnight. Clean any over-spill, and with a wrench or pliers, grasp and gently turn to loosen the bolt remnant.

Welding on a Nut

If the bolt remnant is entirely below the surface or there is not enough of the bolt protruding to grasp onto with any tool, a connection can be made with molten metal, and a nut can be attached to the weld that is attached to the bolt remnant. Once allowed to cool and harden, the nut can be gripped with an Allen wrench, turned and loosened. Considering the tools needed, this is another job that should be done at a metal works or machinists shop, both for safety as well as efficiency's sake.

Center Punch and Drilling

While this can seem like the easiest and most obvious solution, punching or drilling out the bolt hole can damage the threads and the material surrounding the bolt. If you are worried about damaging the item in which the bolt remnant is lodged or if it is a high-value item, the other measures may be a safer bet. Use a drill bit half or three-quarters the size of the bolt diameter or an easy-out bit that has a left-hand twist that grinds easily into the bolt. Make a starter indentation in the very center of the bolt remnant and drill directly down the center. The bolt will either run up its threads and out or can be drilled into thin pieces, which can then be pulled out with tweezers.