Preheat the oven to 400˚F. Scrub sweet potato with a vegetable brush. Puncture the sweet potato with a fork and cook in a pan for 1 hour at 400 ˚F. Blend the sweet potato, pumpkin, carrots, and blueberries while adding water or broth as needed until it reaches a smoothie-like consistency. Pour mixture into an ice cube tray. Pop out a cube whenever your pup wants a cool treat.