The present perfect tense is “has cost” in the third person singular and “have cost” for the other declensions. The past perfect tense is “had cost”.
The future is “will cost”. However, some authors still prefer to use “shall” with the first person (“I/we shall cost”).
I don’t think there is such a word “costed”. Is there? I have looked up three dictionaries and can’t find it in any of them.