Not quite the same texture as a real carrot cake but this will do in a pinch.  Some people don't actually like the texture of real carrots in a cake anyway! Kinda like I am with coconut - ewww, I hate that texture! Throw in some crushed pineapple (drained and as dry as you can get it) and it adds a lot of flavor and texture, too.  Save the pineapple juice and use it in the frosting if you like the flavor, otherwise just drink it! https://www.food.com/recipe/carrot-cake-with-baby-food-carrots-418057