Preheat oven to 350 degrees F (175 degrees C). Line a muffin tin with paper liners.
Mix cake flour and baking powder together in a large bowl.
Strain litchis into a bowl, reserving canning liquid. Pat litchis dry with a paper towel; cut into small pieces. Add 3/4 of the pieces to the flour mixture; toss lightly.
Whisk sugar and egg together in a bowl until sugar is dissolved, about 1 minute. Stir in 5 tablespoons of the reserved canning liquid, butter, and vanilla extract. Add flour mixture; stir batter until just moistened.
Spoon batter into the prepared muffin tin, filling each liner 3/4 full. Scatter remaining lychee pieces on top.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, about 25 minutes.