Spread the drained black beans on a paper towel-lined plate and pat very dry. Let sit a few minutes.
Heat the olive oil, add the leeks, and cook 5 to 6 minutes until softened. Add the garlic and corn, cook 2 minutes more. Let cool slightly.
Mash the dried black beans with a fork until mostly broken down, leaving some texture.
Stir in the leek mixture, egg, breadcrumbs, cilantro, cumin, salt, and pepper until combined.
Cover and refrigerate the mixture for 20 to 30 minutes.
Divide into 8 portions and shape into patties about 3 inches wide.
Heat the neutral oil and fry the cakes in batches, 3 to 4 minutes per side, until golden and crisp.
Drain briefly on paper towels and serve warm.