Combine strawberries and 1 tbsp of the sugar in a medium bowl. Whip heavy cream, remaining 2 tsp sugar and vanilla to medium peaks. Spoon cream into a resealable plastic bag; snip off a corner for piping.
Cut cake into scant ½-thick slices (you will need 24 slices).
Place 1 tbsp strawberries on bottom of each push-up pop mold. Press a slice of cake on top of strawberries, compressing to fit. Add another 1 tbsp strawberries. Pipe a thin layer of cream on top. Repeat layers (cake, berries, cream) to fill molds. Chill 1 hour before serving.