In a pot over medium heat, bring 4 cups of the water to a boil. Add tapioca pearls and cook, stirring regularly, for about 10 to 15 minutes or until translucent.
Remove from pot and using a fine-mesh sieve, rinse under cold, running water. Drain well.
In a pot over medium heat, combine the remaining 4 cups water, coconut milk, and sugar. Bring to a simmer, stirring occasionally, until sugar is dissolved.
Add calabasa. Lower heat and cook, stirring occasionally, for about 10 to 15 minutes or until calabasa is fork-tender.
Using a slotted spoon, emove some of the tender squash. In a bowl, mash with a fork and return to the pot.
Add tapioca and cook, stirring occasionally, for about 3 to 5 minutes or until dessert is slightly thickened. Serve hot.