The Egyptians thought that when pharaohs were crowned, they became gods. So their coronation was their birth. (It sounds fun until you realise there are no sweets.)
The Greeks introduced cake to this custom. Cake? So the Greeks wanted something to honour Artemis, the moon goddess, on their birthdays.
To celebrate the moon, the Greeks baked moon-shaped pastries with lighted candles. That was brilliant!
The first true birthday cake was for children in mediaeval Germany. It was Kinderfest.
Birthday cakes weren't always so tasty. Sugar was scarce and expensive, so sweet cakes were exclusively for the rich.
The Industrial Revolution introduced cheap sugar and other components.
While Wicked Uncle can't send you a cake—we haven't figured out how to mail a whole layer cake with candles