I believe the British Navy issued a 7-barreled volley gun for a few years around the turn of the 19th century. It was .40-.45 caliber and did indeed fire all seven balls at a single trigger pull. The idea was for men in the rigging to fire down onto the enemy deck during boarding operations.
It was abandoned after a few years, largely for two reasons: when fired, it frequently resulted in either dislocating the user's shoulder or flinging him entirely off his perch in the rigging, sometimes both. Not surprising that the sailors hated it.
In fiction, this volley gun makes an appearance in the "Sharpe's Rifles" series by Bernard Cornwell. Sharpe's best friend and sergeant carries one (in addition to his issued rifle) because he is the only man big enough to fire it without injury.
Regards.