For the buttercream: Bring the rum and cane sugar to a boil in a medium saucepan. Add the raisins, remove from the heat, and let macerate for at least 4 and up to 24 hours at room temperature. Strain the raisins, finely chop, and set aside for the cupcake batter. Bring the strained rum to a boil in a small saucepan and reduce to 1/4 cup. Remove from the heat and let cool before adding to the buttercream.
Combine the butter and cream cheese in the bowl of a stand mixer fitted with the whisk attachment, and whip until light and fluffy, scraping the sides and bottom of the bowl once. Add 3 cups of the powdered sugar and whip until light and fluffy. Add the cooled reduced rum and the rum extract and add more powdered sugar, 1/4 cup at a time, and whip until slightly thick, spreadable consistency.
For the cupcakes: Adjust the oven rack to the middle position and preheat the oven to 350 degrees F. Fill mini muffin tins with liners and spray the liners with nonstick spray.
Whisk the flour, baking powder, baking soda, salt, 1 1/2 cups of the sugar, cinnamon, allspice, and nutmeg together in large bowl. Whisk together the melted butter, buttermilk, oil, vanilla, rum extract, and yolks in a medium bowl.
In a clean bowl of a stand mixer fitted with the whisk attachment, beat the egg whites at medium-high speed until foamy, about 30 seconds. With the machine running, gradually add the remaining 1/4 cup sugar; continue to beat until stiff peaks just form, 30 to 60 seconds. Transfer to a separate bowl and set aside. Wash the bowl and dry.
Add the flour mixture to the now-empty mixing bowl fitted with whisk attachment. With mixer running at low speed, gradually pour in the butter mixture and mix until almost incorporated (a few streaks of dry flour will remain), about 15 seconds. Stop the mixer and scrape the whisk and sides of the bowl. Return the mixer to medium-low speed and beat until smooth and fully incorporated, 10 to 15 seconds.
Using a rubber spatula, stir 1/3 of the whites into the batter to lighten, and then add the remaining whites and gently fold into the batter until no white streaks remain. Quickly fold in the reserved raisins.
Fill the cupcake molds 7/8 full and bake until just firm, about 10 minutes. Let cool in the pan set on a baking rack for 5 minutes. Remove the cupcakes from the tins and let cool completely on the racks. Frost with the rum raisin buttercream.
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