Place a small saucepan over medium heat. Stir in sugar, white vinegar, olive oil, salt, and celery seed. Whisk and cook until it boils. Lower the heat a bit and keep whisking until the sugar is dissolved. This will take about 2-3 minutes. Remove the pan from the heat and cool.

In a large bowl, stir together the cabbage, onion, and cucumber. Toss the veggies with the dressing. Chill until ready to serve.