The first-ever reference about the conventional birthday cake dates back in 1746 to a German count's birthday party and not in 1785.
Birthday cakes have been a part of birthday celebrations in Germany since the middle of the19th century (1800). In Germany, adults' and children's birthdays were celebrated with birthday cakes.
However, the link between cakes and birthday celebrations may date back to Egyptians and Greeks. Ancient Egyptians were the first culture to show evidence of advanced baking skills (Food TimeLine). Ancient Greeks made moon-shaped cakes around 1200 BCE-323 BCE. Ancient Romans made cakes for men who had political powers for turning 50 years old.