could write, was able to write
いい作文が書けた?
Were you able to write a good composition?
— 大人は判ってくれない (1959)
何とか今日はお前に手紙が書けた
I somehow managed to write you a letter today.
— パラサイト 半地下の家族 (2019)
もし彼の住所を知っていたら、彼に手紙が書けたのに。
If I had known his address, I could have written him a letter.
書けた
I finished writing it.
書けた?
Did you finish writing it?
— グッバイ、レーニン! (2003)
書けたんです
I managed to write it.
— イル・ポスティーノ (1994)