Debark a bit, take some of the cambium, if it's still fresh (white) and smells like fresh green bean pods or green peas, it's likely a locust. Pretty poisonous if it's black locust, so no need to taste it.
If it's dry or brown (dead), tear some fibers from it. (Black) locust will give you very long and flexible fibers. Put some in a cup of hot water, if it smells again like bean pods, it's likely locust. Mulberry will never have that smell. It could be dead already for too long though and not give that smell anymore.
The bark doesn't seem typical for black locust of that size, the flakes look too thin for that size, ridges not deep enough and the color seems too grey instead of light brownish grey. Looks more like honey locust to me.
Don't know the smell of honey locust cambium, but since it's a leguminous tree too I bet it also has a smell of fresh peas.
Still, could also be Kentucky coffee tree, another one in that family with similar looks.
