Place strawberries in a blender along with sugar (if using). Blend until smooth. Set aside ½ cup mixture, then add coconut milk and water to the remainder. Blend until combined.
Divided blended strawberries between 6 ice-block moulds. Add strawberry milk mix. Use a skewer to swirl the blended strawberry through each ice block.
Place in freezer for 6 hours or overnight to set.
Remove from moulds to serve.