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If this is a reocurring problem, and not just a single failure, there are a few things that you can try:

1. Change the type of pan you're cooking in. A dark metal pan or a clear glass pan will cook the bottom faster than a shiny metal pan.
2. Place the cake lower in the oven, so that the bottom is closer to the heating element.
3. Shield the top of the cake so that it cooks slower, by placing a sheet of aluminum foil or a sheet tray on a rack above the cake. (note, don't cover the cake, we're just shielding it from radiant heat).
4. Put less batter in the pan. Spread it into two pans, and stack them together once baked.

And if none of that helps, you can also try cooking the cake at a lower temperature for longer ... it'll end up more dense as you won't get the oven spring, but it'll help prevent the chance of over-baking it. You can also start it warm, but then lower the temperature 25-50°F once it's been in for a few minutes.

Consider that commercial industrial bakeries would be highly motivated to reduce baking time if it was feasible, at least in a money saving manner.

And yet the equipment for continuous process baking uses approximately the same temperatures and times used at home, just with continuous rather than batch oriented equipment, and with a higher degree of precision and ability to repeat consistently.

One therefore concludes that the traditionally known times are at least approximately optimal in terms of outcome and energy (or at least cost).

In some sense, cookies (historically, the word comes from a term for "little cake") are your speed baking answer. They bake in 12-18 minutes typically, compared to full sized cakes which bake in a time on the order of an hour.

By reducing the size of the food item, the time to cook through is reduced.

Very small cookies (thumbnail sized) can bake through in 5-8 minutes or so, but are terribly tedious and difficult to portion out accurately enough to get consistently good results at home.