Prepare an 8.5x4.5" (one pound) loaf pan by greasing it and lining the bottom with parchment paper. Set aside. Move the oven rack to the middle position and heat the oven to 325°F.
If you're using full-sized gumdrops or jujubes, prepare them by cutting them into small pieces (I cut each gumdrop into about 6 pieces). Toss the gumdrops (including baking gums) with 2 Tablespoons all-purpose flour. Set aside.
Whisk together 1 cup all-purpose flour, ½ teaspoon baking powder, ½ teaspoon baking soda, and ½ teaspoon salt in a medium bowl. Set aside.
Add ½ cup unsalted butter and ¾ cup granulated sugar to the bowl of a stand mixer fitted with a paddle attachment (or to a large bowl). Cream the butter and sugar together on medium-high speed until well combined. Add 4 ounces cream cheese and cream it into the butter-sugar mixture until light and fluffy. Scrape down the sides of the bowl.
Add 2 large eggs, one at a time, beating the mixture until well-combined and scraping down the sides of the bowl after each addition. Add 1 Tablespoon lemon juice and ½ teaspoon vanilla and beat again until well combined.
Add the flour mixture and mix on low speed until no loose flour remains. Increase the mixer speed to medium and mix for about 1 minute until completely combined.
Fold the gumdrops, as well as any loose flour that remains with the gumdrops into the batter, mixing gently until no pockets of flour remain. Note that the batter will be quite thick.
Spread the batter into the prepared loaf pan. Bake for 65-70 minutes, until the top is golden brown and a toothpick comes out with a few crumbs clinging to it. Avoid opening the oven during cooking, or checking the cake too early to prevent the loaf from sinking. Place the pan on a wire rack to cool completely before removing from the pan.
To serve, sprinkle the cake with powdered sugar, or make a simple glaze if desired. Cut into slices. Store any leftovers in an airtight container or zipper bag at room temperature for up to 2 days, or in the freezer for an extended period of time.
Notes
I used Ganong AB Gums, which my parents purchased in Nova Scotia. Dare has a similar product, called Juicee Gumdrops, or a similar Christmas version.For minimal prep, simply use baking gums, which are much smaller and don't require cutting (still toss them with flour though). Note that you should be able to find these in the baking aisle, or Bulk Barn during the holiday season (and maybe all year). To my American friends: it seems that a lot of the gumdrops available on your side of the border are spice-flavored, and I don't think that would be a good option. In your case, I would recommend using regular jujubes, and cutting them into pieces. Whichever gumdrops you use, make sure to taste them before you add them to your cake. The ones I used had a mint-flavored color, which would not pair well with the fruit - I removed them. Similarly, I would recommend removing any black licorice ones.