First of all many thanks for posting such an interesting topic. I guess it will help users in here to understand and differentiate the different tenses a main verb may take

Concerning the tense of your sentence

They will have been building the hospital



They: pronoun acting in here as the subject of the sentence
Will have been building: auxiliary verb+ the present participle of the main verb ( future perfect continuous or progressive)
The hospital: direct object


and below you will find he sentence I'm sharing with you, try to find the tense and the function of the whole sentence.

I would have believed you if you had said the truth.