Dreaming about a cub represents that one is just out of an initial phase and wants to explore their new identity, but it may also be a metaphor for the growing pains and stresses of leaving behind what one knew before. It parallels our waking lives, such as comfort and dependence maybe just like how puppies would be to their parents as kids.
When you dream of an animal cub, it also takes away some aspects of your personality. The young creature itself can symbolize something about your life, such as elements that can justify your fears or limitations put up in the waking world.