Bundt Cake

If you are an accomplished baker and/or adventurous, go with the old cake recipe in a new shape (Bundt pan). But they are sometimes tricky, and if success is important, maybe stay with the tried-and-true pan.
If you go for the Bundt cake, do a few things ---
1) compare the volume used by the original recipe and the Bundt cake. If the same, fine. If not, multiply up or down to prepare enough but not too much batter.
2) see a chart comparing cake pan volumes to decide #1. For example:
http://dish.allrecipes.com/cake-pan-size-conversions/
3) be sure to prepare the Bundt pan (even if it is non-stick) before you pour in the batter. they are often harder to release perfectly than regular pans. Most call for butter and flour, but often the flour shows after the baking. Other suggestions to use (depending on the flavor of your cake) are cocoa, bread crumbs or cake crumbs instead of the flour.

Ooh fun! What's the cake recipe? My thought is that you'd need to make more batter, but it really depends on your recipe and the pan that you're meant to be baking it in in the first place.