Heat the oven to 350 degrees and grease a 9-inch loaf pan. Beat the sugar and butter with the paddle attachment of a stand mixer (or with a handheld mixer) until light and fluffy. Add the bananas, eggs and vanilla, and beat until well combined.
In a separate medium bowl, combine the flour, baking powder, salt and cinnamon. Chop or tear the marzipan into small pieces and add to the flour mixture, stirring to coat each piece with flour and prevent the marzipan pieces from sticking together. Stir in the chocolate chips if you're using them. Add the flour mixture to the butter mixture and stir just until combined.
Transfer the batter to the greased pan, and bake until the top is golden brown and a toothpick inserted into the center of the loaf comes out clean, 45 to 60 minutes. Cool thoroughly, then slice and serve. (Store leftover banana cake wrapped in foil or plastic wrap at room temperature for up to a few days.)
Nutrition information per slice: