書けた

could write, was able to write

→ 書ける
書け can write, be able to write + Past tense
verb · past potential Rare #31,464
could write, was able to write
JA: 昨日、手紙が書けた。
EN: I was able to write a letter yesterday.
Conjugation of 書ける
Potential past
書けた

いい作文書けた

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.

— 大人は判ってくれない (1959)

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)