They probably won't be in the heartwood of the mulberry. For future reference, if for some reason you do something similar and don't seal a piece up (or it is sealed and bugs start to get in anyway), you can heat box the wood for about 2 hours to kill the insects. There are actually a few pest control companies who do this for houses and furniture. As long as the temperature within the wood gets to 150degrees for over 30 minutes, it kills the insects as it brings them past their critical point for heat. Of course, you'd want to do this as soon as noticing insect damage, not after there is a pile of fine saw dust underneath your stave. At that point, they've gotten well past the sap wood and your wood is now firewood. Another thing you could potentially use is pine tar. The only reason I mention it is it works and you can produce this yourself...which is something many people in this group are interested in.