Yes, the baby in the king cake represents Jesus!
The King Cake and the baby in it represent Jesus. The baby is in the cake as a symbol of birth and renewed life. The cake is called King Cake in reference to Jesus.
A king cake is a traditional cake served and eaten on Mardi Gras. Typically it is in a round shape, is a plain cake (like angel food, vanilla, or pound cake), and is decorates with a very sweet icing. Often, the decorations and icing colors are done up to match those of Mardi Gras (green, gold, and purple). There is a little toy baby or "king" buried into the cake. Whoever finds the baby is considered to be lucky and is "king" (or queen) for the day.
On Mardi Gras one of the most famous desserts to be eaten is King Cake. The reason it is called King Cake is because of the baby Jesus that is hidden within it. Whoever finds the baby in their slice of cake is sometimes crowned King for the day, are told they will have luck, and they have the honor of buying the next cake for the next party. So the baby represents a lot of different things.
Only on the Baby
The King Cake is the Mardi Gras specialty in New Orleans, Louisiana.
Usually just the baby goes into a King Cake. Sometimes people put a small coin (penny or dime) or a thimble in, too, though.
The official dessert for Mardi Gras is the King cake. It is a tradition that is from New Orleans. During Mardi Gras people will have parties where everyone will get a piece of King cake. Inside the cake there is a hidden baby (normally its a very small plastic one). The person who find the baby in their cake has the responsibility of buying the next King cake.
The person who finds the baby in their slice of King Cake is traditionally responsible for bringing the King Cake to the next party or gathering. They may also choose to throw next year's Mardi Gras party.
Person who finds Baby Jesus buys the next cake
Typically it means you have to purchase the next King Cake. However, some families apply house rules, so the meaning is left up to the group.
Traditionally, a small plastic baby doll (only an inch or so long) or "king" is hidden inside the king cake.