It actually sounds like you're describing pokeweed, but the photo is Paulownia tomentosa, a weed tree. Paulownia flowers in spring with purple bell shaped flowers before the leaves appear and has round seed pods in fall, not berries.

And I just noticed a red stem on the ground behind your tree. That's probably the pokeweed that you saw last fall.

Wow, you have good eyes. Yes, that was pokeweed that I took down. I didn't know it at the time! It was getting too tree-like and it was right against the foundation of the house.

I guess I have to take down the Pawlonia, too. That's a shame -- the flowers are very pretty.

Thanks very much for your help!

Privess/Pavlonia trees are actually not ugly. The grow perfectly straight, have very values wood, and have these terrific blue candle like blooms, like a chestnut bloom, but in blue. They transplant well, and grow relatively fast. They are, however proliferous, i.e. invasive. I have two and I like them, but any more I'll eradicate.

They also get bigger than a house! but I agree, when in bloom they are beautiful.

Is it true that Pawlonia trees are often stolen for their prized wood?

Paulownia has become a weed nuisance, it comes up in waste places. I spoke to the guy who works on my chainsaw recently, he said noone has cut Paulownia in 25 years, no market. See link on trees forum. Usually novice gardeners are attracted to the freakish leaves but experienced gardeners know to avoid this species.

Here is a link that might be useful: Paulownia Thread