The term "cook" is more commonly used when referring to preparing a mug cake in the microwave. While the word "bake" traditionally refers to cooking in an oven, when it comes to making a mug cake, the cooking process is generally quick and done in a microwave.
Microwave mug cakes are a popular and convenient way to make single-serving cakes quickly. The ingredients are mixed directly in a microwave-safe mug, and then the mug is placed in the microwave to "cook" the cake. The cooking time is typically just a few minutes, which is much faster than traditional baking in an oven.
So, in summary, it is more appropriate to say "cook" a mug cake in the microwave rather than "bake."