DX- first does this happen occasionally…??. Well if it does then you probably have some dawn piped hormones, which you need to increase your basal.
On the other hand, it is probably because you ate some high carby breakfast like cereal, bagel or pizza whatever it is the high carb food will keep your sugars high for about 2-3 hours (which in your case you ended up being 60 a few hours later probably in result to the food) or even never come down.