Combine the raspberries with 1 cup of the water (the rest of the water will create your lemonade in a few steps).
Mash the berries with a potato masher or fork.
Bring them to a boil and then immediately reduce to a simmer. Cook until everything has cooked down by about half.
Allow them to cool for a bit and then transfer to a fine-meshed sieve over a bowl.
Use a large spoon or other slightly curved surface to mash the raspberries through the sieve. This will remove your seeds and pulp.
You will be left with a bowl of raspberry juice that has a small amount of fiber in it (usually scraped from the bottom of the sieve when you're done mashing).
Combine this in a pitcher with the remaining 6 cups of water and all other ingredients. Adjust sweetener to taste and serve over ice for a nice chilled glass of fresh, homemade lemonade.
Please note that the nutrition data given here is a ballpark figure. Exact data is not possible.