Just use "書けます"。 The expression "書くことができます" could have been born to understand the English expression "I am able to...." wordly. We do not have such expression, as we do not say "書くことが可能です"。 But it is very practical for Japanese learners, because their languages have modal verbs, almost without exception. As Amano san says, Japanese would rarely use "書くことができます"

I'd say that 書くことができます is not a real Japanese even it seems grammatically correct. You could only hear 書けます in formal or neutral situations and 書ける and 書けるか? in rough talk. If your concern is about an ABILITY of 書く, you could say 書く能力があります , but might be rare, which means literate in most cases.

To see the difference (assuming there is one), just think about this question of mine: "what is the difference between: "I can write" and "I'm able to write"?". If you could see a difference between those two, you would probably see the difference between 書けます and 書くことができます. At the end of the day, if there was a difference, then that would just be that 書けます is more conversational and 書くことができます is more formal. Good luck.