Sugar !

Whether or not your burned it afterwards doesn't really matter. Chocolate cake is yummy. Eating it once in a while, even 600 calories of it, won't put you too far off your goals (or smaller portions that fit within your calories on a more regular basis). Consider, even if that 600 calories was all on top of your regular calorie goal, if you did it just once, you'd still be in a 2900 calorie deficit for the week, assuming you're going for 1 lb per week lost. You might lose less than a pound, or you might end up compensating for it by eating a bit less on the other days (I'm 50-100 calories under some days without even trying).

The bigger issue is how you look at food. Since your topic title is sugar, I would guess you think the cake is bad for you because it has sugar/is "junk" food. (Plus the idea that it's a "big mistake.") It's not. It's food. In general, you want to aim for a mostly nutrient-rich diet, for health, but for weight loss it's calories that matter. There isn't really and "bad" foods, just foods that have more or less calories, more or less nutrients. It's okay to fit some "treats" into your daily diet and calorie goals. For long-term sustainability and mental health, it may even be better than a strict, no "junk" diet (YMMV)

ETA - since you exercised for around 800 calories (could be more, could be less, it's hard to be super accurate) it balances out those calories. But please, don't use exercise as punishment for eating something. Exercise is great for health, physical and mental, and helps to increase deficit, so keep exercising. It just can become a problem if you try to use it to "undo" the stuff you feel guilty for eating. (I hope that makes sense. I'm not criticizing today's decision, just trying to put it in perspective for future healthy habits)

I ate 1100 calories of chocolate lava cake in one sitting a couple of weekends ago. It'll be okay. Just don't do it all the time.