Nash said the bill from another parent sought 15.95 pounds ($24.00) because his son Alex had not attended the party at a ski centre in Plymouth, southwest England.
Nash told the BBC on Monday he had initially accepted the party invitation, but later realized Alex was supposed to visit his grandparents that day. He said he did not have contact details to let the other family know.
The birthday boy's mother, Julie Lawrence, told the BBC that her contact details were on the party invitation.
Nash says Lawrence has threatened him with small claims court but he has no plans so far to pay.