You already know the answer. You're just not getting enough sleep. I bet on those days when you go to bed at 10pm but "still feel tired, although not as much" you're simply not recovered from those days before when you only got 6 hours.
It's that, and that the OP's body is accustomed to going to sleep around midnight. Going to bed occasionally at 10 won't be the same as refilling the sleep bank, because his body won't be ready for sleep.
Get in the habit of going to bed early, if you think that's the answer. Since your commute is only 7 km, unless it's all up a very steep hill, it isn't the exercise that's wearing you down, it's getting up early to do it.