In a large pot, bring water to a boil. Add the cubed sweet potatoes and cook until tender, about 15 minutes. Drain and let cool slightly.
In a large mixing bowl, mash the sweet potatoes with a fork or potato masher until smooth.
Add the black beans to the bowl and mash them lightly, leaving some whole for texture.
Stir in the breadcrumbs, red onion, cilantro, garlic, cumin, chili powder, salt, pepper, lime juice, and mix until well combined.
Form the mixture into patties, about 1/2 inch thick. You should have about 8 patties.
Heat olive oil in a large skillet over medium heat. Cook the patties for about 4-5 minutes on each side, or until golden brown and crispy.
Serve warm, garnished with additional cilantro and lime wedges if desired.