The network released a statement saying, "We failed to spot the offending material within it."
The video was by a musical theater group Barbershopera who appeared as guests on the show early this morning.
They aired the music video to the song, "I Could Have Married Kate," which featured a snippet of the royal with obscene doodles on his face.
In what appears to be the official engagement photo of Will and Kate Middleton, the new father was shown with glasses, a moustache and goatee, and a blacked-out tooth in addition to the X-rated drawing.
Kensington Palace announced on Wednesday that the new dad will attend the Anglesey Show on Aug. 14.
At the event, the Duke of Cambridge will watch gundog and falconry displays and meet with local young farmers. He is also scheduled to view some cattle judging before moving to the central show area, where he is expected to make a short speech.
The Anglesey Show is the largest two-day agricultural event in North Wales and attracts more than 56,000 people. William, an RAF rescue helicopter pilot at Valley on the island, will attend the show's second day.
The new family of three is currently staying at the Bucklebury home of the Duchess of Cambridge's mother and father.