Add drained and rinsed beans to a large bowl. If you want to only make a three bean salad, you can remove one of the varieties of beans and have two cans of your favorite bean.
If you find raw red onion to be rather strong, you can soak the cut slices in cold water for about 30 minutes and then draining before adding to the salad. This step is optional but encouraged. Add onions and cucumbers to the bowl with the beans.
Add the dressing ingredients to a small bowl and whisk together until all of the sugar has dissolved. Taste and adjust sugar and/or salt if desired.
Add dressing to salad and gently toss to combine, taking care not to crush the beans. There will be excess dressing at the bottom but that is what you want because it tastes so good. Give it a good toss just before serving if some time has passed.