cleaning wood

use a hair dryer to warm up the glue

wood table

The reason carpenters use glue as well as nails on trim work is that the glued joint is actually stronger than the wood itself. You can try heating it up, but you may end up just prying the block off of the table and having to repair the damage that results. Good luck.

wood type

you say white glue not yellow. white glue is more for paper products and crafting. If possible take a block of wood that you can hold safely with one hand and place one end against the glued block and smack the end with a hammer. go with the grain and use hard blows with hammer. this might release the glued block. if not use a chisel and hammer and tap into glue seem.

exotic wood

Most, not all, but most white glues are water soluble. I would try soaking it with water. You have to keep it wet and let the water soak into the glue. An easy test is to lay a wet cloth at the joint. If the glue squeezed out becomes cloudy the trick will work. The problem is it takes time, lots of time. It could be a week or more but it will eventually release. If you can turn the table over it will make the job easier.

Using a block and hammer blows to shear the two pieces apart as described above can be used in conjunction with the soaking process I described. You just have to be very patient. Soak for a day or two then hit it one solid blow. If it comes off fine, it not keep soaking and striking it on a daily basis.

Good luck.