The correct passive form of the given sentence is A lot of coffee was drunk by him before the marathon.

The active voice of the sentence is "He drank a lot of coffee before the marathon." This sentence is in the simple past tense, which is used to describe an action that happened in the past. The passive voice of the sentence is formed by putting the subject of the active sentence after the verb "to be" and the past participle of the main verb. In this case, the subject of the active sentence is "he" and the main verb is "drink." The past participle of "drink" is "drunk." So, the passive form of the sentence is "A lot of coffee was drunk by him before the marathon."

The other options are incorrect because:

• A lot of coffee is drunk by him before the marathon. This sentence is in the present tense, but the action of drinking coffee happened in the past.
• A lot of coffee was drunken by him before the marathon. The word "drunken" is not a correct form of the past participle of the verb "drink." The correct form is "drunk."
• A lot of coffee had been drunk by him before the marathon. This sentence is in the past perfect tense, which is used to describe an action that happened in the past before another action happened. However, in this case, the action of drinking coffee is not relevant to the present.