Carrot Cake's first ability will trigger whether you sacrifice it to pay the cost of its own last ability or due to another cost or effect. For example, if you sacrifice Carrot Cake in order to forage, you'll still create a Rabbit token and scry 1. It's delicious no matter how it's served!

Whatever you do, don't eat the delicious cards.

Food is an artifact type. Even though it appears on some creatures, it's never a creature type.

You can't sacrifice a Food to pay multiple costs. For example, you can't sacrifice a Food token to activate its own ability and also to activate Maraleaf Rider's ability.