Both sound natural. They are very similar in meaning, though a native speaker is likely to use them with this nuance: 1. "I did it for your own good." = "You may think what I did is not what's best for you. However, I see the situation differently and did what I know to be best for you." 2. "I did it for your sake." = "I did this primarily because it is what you would have wanted me to do." (On my own, I might have chosen something different.) I hope that helps!

You can use both Daniel.

Yeah, they are both correct and natural. “For your own good” and “for your (own)sake” have similar meaning.

Both are correct and equally natural to say.