Has an Euros game ever ended 8-1?
Yes. Euros has seen a final score of 8-1 3 times. It first happened on October 19, 1975, when Hungary beat Luxembourg, and most recently on September 7, 2015, when Poland beat Gibraltar.
That makes 8-1 the 26th most common final score out of 34 that have ever occurred in Euros. One point away, 9-1 has happened 1 times and 8-2 has happened never. At one point the score disappeared for 37 years, between 1978 and 2015.