Fill each mold with coconut water approximately 2/3 full.
Place the lid on the mold and insert sticks into each slot. Place the popsicle mold with coconut water in the freezer for two hours or until the coconut water is in a slushie state (somewhat frozen but not completely).
While the coconut water is freezing, remove 10 blackberries from the package (approximately one third to half). Cut each of those 10 blackberries in half. Set aside. (If the blackberries are large, use 10 for this step. If small, use more as needed not to exceed half of the package in total).
Make the blackberry puree. Mash the remaining blackberries that you have not set aside in a small bowl. Mix with the sugar. Set aside.
When the coconut water has turned to a slush, remove from the freezer. Use the popsicle sticks to guide some of the blackberry halves into each popsicle (two halves or more per popsicle). Add one Tablespoon of the blackberry puree into each popsicle mold, leaving a gap of just 1/8-1/4" at the top so that it has room to expand. Use the popsicle stick to move the puree and berries throughout the mold to get your desired effect (See note).
Replace the lid and readjust the popsicle sticks. Make them as straight as possible so it is easy to get the lid off when frozen.
Freeze until completely solid, preferably overnight, typically at least 2 hours longer.
I used this popsicle mold.This recipe fills 10 popsicles, 3 oz each. Different molds may have a different size and require more or less ingredients.Blackberries can be a little tart. For a sweeter popsicle, add more sugar or use strawberries. You can use either frozen or fresh berries. If using frozen, defrost the berries first.You can also add the puree immediately when you pour in the coconut water, however the puree will likely sink to the bottom. This makes it easier to assemble as you do not need to keep track of when to add the blackberries, but it will be more of a layered effect instead of mixed.