It is possible to bake a cake in a microwave oven. While it is not possible to use metal cake pans in a microwave, silicone bakeware is safe for use in microwaves and is recommended for use when baking a cake in the microwave.
Which.co.uk, a website that gathers and investigates consumer products and reviews, indicates that almost any cake recipe is suitable for microwave baking. Cakes baked in microwaves are often less moist than those baked in a conventional oven, so it is important to take care not to bake a cake for too long to insure it retains as much moisture as possible. Silicone cookware is recommended for baking cakes in a microwave because it is easy to clean in addition to being safe for microwave use.