Combine the figs, apricots, raisins, rum, orange zest, and lemon zest in small bowl; cover with plastic wrap and let sit at room temperature for at least 4 hours or as long as overnight.
Heat oven to 350°F Grease the bottom and sides of a 12 1/4" x 4 1/4" x 2 3/4" loaf pan with butter and dust all over with flour; tap out excess flour and set aside.
Combine butter and sugar in a large bowl and beat with a handheld mixer set to medium speed until the mixture is pale and fluffy, 1-2 minutes. Add the eggs one at a time, beating well after each addition. Add the reserved fruit-rum mixture and the flour mixture and mix on low speed until just combined.
Transfer batter to prepared pan and smooth the top with a rubber spatula. Bake until a toothpick inserted into the middle of the cake comes out clean, 40-45 minutes. Unmold cake onto a wire rack and let cool completely before slicing.