Thanks for all the replies and PMs guys, I really appreciate it. I have to say, though, I wasn't questioning the workmanship, just the curiousity factor concerning the glue that was used, as I hadn't seen a poly glue that was soft on the outside and turned yellow instead of being amber.
That being said, brianna187 nailed it with Elmer's poly, I am pretty sure. I had a bottle of it that I picked up to fix some chairs and hadn't got to them yet. On Kelly_guy's advise, I tried it in a mahogany butt sleeve piece with a maple core and the results on the outside was exactly as my original pic. Last nite I cut it in half and found a great bond, no gaps or foam. I could see where it absorbed into the mahogany, and hardened. It took a full day to harden on the outside, and now that it's cut in half, I tried to pry the core half out and it won't budge. I am really impressed. It took about 4 hrs to set up to the touch, but I followed the instructions and moistened the wood and then really gooped it in the hole and on the core. I tried to get good pics, but my camera won't focus close enough for the pic to be worth any for inspecting. Thanks again for the help, and once again I apologize to anyone that I may have unintentionally offended.
Dave