Talk about an extrovert.

Dolly Parton once fooled a marching band into thinking she was old friends with their director — even though the two had never met.

Nathan Hickman, the band director at Parton’s alma mater, Sevier County High School, told The Post that he first met the country legend in 2013, when his students played a Dollywood concert in nearby Pigeon Forge.

“My students asked if I knew her,” said Hickman. “Of course, I said yes and that we had been friends for years… Truthfully, I had never met her.”

Apparently, Parton overheard the exchange and knew immediately how to make the high school band teacher into a hometown hero. “When she…

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