Preheat the oven to 350°F (175°C). Line a muffin tin with cupcake liners.

In a mixing bowl, cream together the butter and sugar until light and fluffy.

Add eggs one at a time, mixing well after each addition. Stir in vanilla extract.

Gradually add flour and mix until just combined.

Spoon the batter into the prepared muffin tin, filling each liner about 2/3 full.

In another bowl, beat the cream cheese until smooth.

Add sour cream, sugar, lime juice, and mashed blackberries. Mix until well combined.

Spoon the cheesecake filling over the cupcake batter in the muffin tin.

Bake in the preheated oven for 20-25 minutes or until a toothpick inserted comes out clean.

Allow to cool before serving.