agree with others, looks like magnolia. the ones that grow around here have hard red seeds about the size of pop corn (different shape though), strong smelling white flowers, thick leathery leaves that make a mess and are slow to break down (why lots of people do not like the tree in their yard), smooth bark...
yup magnolia. back home they grow plentiful and large. they seem to like a hot humid environment. as kids we would chuck them things at each other pretending they were grenades.
Magnolia. Around here, ( z6 tn) the squirrels will get most of the seeds, jaybirds the rest. If you want to save seed to plant, collect them as soon as they're red and visible in the cones on the tree, don't wait till they drop.