I believe this fast growing tree with huge leaves is a princess tree. Also called Empress Tree or Royal Paulownia, the scientific name for the tree is Paulownia tomentosa.

Young Princess Trees

The tree is desired by some for its purple flowering display in the spring. Originally from Asia, the tree is considered invasive as its seeds can travel a long distance spreading itself.

The young trees take several years before they present purple flowers, but here is a picture of a mature princess tree growing along the Fairfax Country Parkway. There are also flowering princess trees visible each spring from I-66 in Thoroughfare Gap.

Princess Tree along Ffx Co Pkwy