When Billy Costa asked four Brookline High School contestants on the latest showing of WGBH’s “High School Quiz Show’’ “What’s your favorite film and why?’’ the host got four answers that all had one bizarre common denominator: Nicolas Cage. Right down the line, each student rattled off a Cage film _ “Con Air,’’ then “Face/Off,’’ then the “National Treasure’’ films, and finally “Raising Arizona.’’ Costa chuckled and said to the Cage-y guys: “Beautifully done. Very eloquent and so profound. Thank you all of you.’’ We could not help being a little suspicious, as if it was pre-planned. Especially when the last kid referred to the “powerful performances’’ in “Raising Arizona.’’ Needless to say, that video has now gone viral.