Add sugar, water and corn syrup to a saucepan. Attach a candy thermometer to the side.
Boil and allow sugar mixture to reach the soft ball stage (235-340 degrees F).
While the sugar is coming up to temperature, whip the egg whites in a stand mixer with the whisk attachment. Whip them to a soft peak.
With the mixer on medium speed, carefully pour the syrup down the side of the mixing bowl. Turn the speed up to high and whip until the meringue is at a stiff peak and room temperature. You can speed up this process by wrapping the outside of the bowl in ice packs or cold wet towels.
When the meringue is cool, slowly add the soft butter while mixing on high.
Once all of the butter is incorporated, add the cinnamon, vanilla and rum (and eggnog if using).
Notes
Before serving the cupcakes, top them generously with a mixture of fresh grated nutmeg and cinnamon. This will enhance the eggnog flavors.