No, there's absolutely no reason you can't cut a birthday cake before your actual birthday.
There's a common misconception that cutting a birthday cake before your birthday brings bad luck, but this is simply a superstition. The idea of "luck" itself is debatable; many consider it to be coincidences and serendipitous events that seem related but are actually independent.
Therefore, go ahead and cut the cake whenever you want! Whether it's for an early celebration, to avoid wasting cake, or simply because you feel like it, there's no evidence to suggest any negative consequences. Enjoy!