Has a College Football game ever ended 105-3?
Exactly once. On November 3, 1923, Utah beat Albertson 105-3, and no College Football game before or since has ended that way. When it happened it was a scorigami, the first 105-3 in league history.
That makes 105-3 the 1819th most common final score out of 2,215 that have ever occurred in College Football. One point away, 106-3 has happened never and 105-4 has happened never.