3.1  τούτου χάριν ἐγὼ Παῦλος ὁ δέσμος τοῦ Χριστοῦ [‘Ιησοῦ] ὑπὲρ ὑμῶν τῶν ἐθνῶν

τούτου χάριν – The prepositional phrase has a conjunctive nuance, linking what follows with what precedes (“for this reason”). Presumably the new status of non-Jewish Christians explained in the previous paragraph is the reference.

ἐγὼ Παῦλος ὁ δέσμος τοῦ Χριστοῦ [‘Ιησοῦ] — ἐγὼ is the subject of an implied verb, perhaps the one used at the beginning of v. 14. Two appositional structures follow – Παῦλος,  ὁ δέσμος, which modify the subject.  The writer is emphasizing this subject. The genitive τοῦ Χριστοῦ defines the person who controls ὁ δέσμος.

ὑπὲρ ὑμῶν τῶν ἐθνῶν – The prepositional phrase describes the group “on behalf of whom” Paul’s implied action is taken. The genitive τῶν ἐθνῶν is appositional to ὑμῶν.

3.2 εἴ γε ἠκούσατε τὴν οἰκονομίαν τῆς χάριτος τοῦ θεοῦ τῆς δοθείσης μοι εἰς ὑμᾶς,

εἴ γε ἠκούσατε – The conjunction εἴ marks a first class condition which includes an aorist indicative verb. The particle γε (enclitic), usually appended to a term that it is referencing, directing attention in some way to it. In this case it would be the conditional element, “if indeed…” Perhaps marks a change in pitch in the speaker’s tone. The aorist indicative verb aspectually indicates a completed action. So Paul assumes his audience has heard about the information he will share.

τὴν οἰκονομίαν – Direct object of the verb. Here it probably has the idea of a concept, plan, arrangement that is made and implemented (cf. 1:10; 3:9).

τῆς χάριτος τοῦ θεοῦ τῆς δοθείσης μοι εἰς ὑμᾶς – τῆς χάριτος may be an objective genitive, which would make the display of favour the outworking of the plan. Alternatively it might be a subjective genitive in which “grace” is the subject, implementing the plan. It is qualified by the adjectival participle τῆς δοθείσης which in turn is modified by an indirect object and a prepositional phrase, that defines who receives the benefit of this work of grace. The participle is aorist in tense form and probably then refers to a completed action. No agent specifically is identified regarding the passive voice. τοῦ θεοῦ identifies who shows this favour, but it may also be classified as a subjective genitive, i.e., the favour exercised by God. Defines the goal of the plan.

3.3 [ὅτι] κατὰ ἀποκάλυψιν ἐγνωρίσθη μοι τὸ μυστήριον, καθὼς προέγραψα ἐν ὀλίγῳ,

[ὅτι] – The originality of this conjunction is uncertain. Note that p46 and B witness to it, but א A do not. If it is original it marks the dependence of the material in v.3 on the prior ἠκούσατε, forming an objective clause of indirect discourse and perhaps functions appositionally to οἰκονομίαν. If it is absent, it means that the material in v. 3 forms an independent clause.

κατὰ ἀποκάλυψιν – Adverbial prepositional phrase which modifies ἐγνωρίσθη and indicates a standard. Its position gives it prominence in its clause.

ἐγνωρίσθη μοι τὸ μυστήριον – The aorist passive verb indicates a completed action that the context places in the past. The subject of the verb is τὸ μυστήριον. Is there a connection between ἀποκαλύψις and μυστήριον?

καθὼς προέγραψα ἐν ὀλίγῳ — A subordinate comparative clause, marked by καθὼς. The main verb is aorist active indicative, modified by the adverbial prepositional phrase describing the “brief” comments he previously has provided about this subject. Is this a reference to material in Eph. 1-2 or to a previous piece of correspondence?

3.4  πρὸς ὅ δύνασθε ἀναγινώσκοντες νοῆσαι τὴν σύνεσίν μου ἐν τῷ μυστηρίῳ τοῦ Χριστοῦ,

πρὸς ὅ… ἀναγινώσκοντες – A relative clause which defines the previous communication referred to in the prior clause. The adverbial prepositional phrase modifies the present active participle, i.e., “reading concerning which….” The present tense form suggests that his audience is currently reading this material in this letter or is reviewing this material as they are reading the current letter.

δύνασθε… νοῆσαι τὴν σύνεσίν μου – The main verb is present middle indicative, qualified by complementary infinitive. The information Paul provides about his personal background “enables them to comprehend/understand.” The aorist active infinitive governs a direct object “my insight” and the genitive pronoun probably is subjective genitive here.

ἐν τῷ μυστηρίῳ τοῦ Χριστοῦ — This adverbial prepositional phrase could modify the noun σύνεσίν (my insight into the mystery) or the infinitive (to understand in reference to the mystery my insight).  The genitive is probably descriptive, indicating the content of the “mystery.”

3.5  ὃ ἑτέραις γενεαῖς οὐκ ἐγνωρίσθη τοῖς υἱοῖς τῶν ἀνθρώπων ὡς νῦν ἀπεκαλύφθη τοῖς ἁγίοις ἀποστόλοις ἀυτοῦ καὶ προφήταις ἐν πνεύματι,

ὃ … οὐκ ἐγνωρίσθη – Another relative clause and the antecedent of the relative pronoun is probably τῷ μυστηρίῳ. The pronoun is the subject of the verb (aorist passive indicative).

ἑτέραις γενεαῖς – Probably a dative of time, i.e. “in other generations.” However, it could mark an indirect object, which is then defined appositionally by the following dative noun, i.e., “to other generations, the sons of human beings….”

τοῖς υἱοῖς τῶν ἀνθρώπων – Based upon the previous comment it could be either the indirect object of ἐγνωρίσθη or an appositional modifier of ἑτέραις γενεαῖς. The phrase is unusual, expressing a Semitic idiom, and refers to human beings in general.

ὡς νῦν ἀπεκαλύφθη – An adverbial comparative clause marked by ὡς. The adverb νῦν positions the action in present time, even though the verb is aorist passive in tense form. This suggests a very recent action that is completed, but quite contemporary.

τοῖς ἁγίοις ἀποστόλοις ἀυτοῦ καὶ προφήταις – The dative marks the indirect object of the main verb and identifies the recipients of the ‘revelation’. The article covers both nouns and this is an example of the Granville Sharp rule. The genitive pronoun is probably functioning to identify the “source” or “authority” for such individuals acting in this capacity. Do these two terms refer to one and the same group, i.e., apostles who also are prophets, or to two different groups both related to God? Does Paul include himself in this group (cf. Eph. 1:1)?

ἐν πνεύματι – Adverbial prepositional phrase defining the means by which this revelation has been provided.

3.6  εἶναι τὰ ἔθνη συγκληρονόμα καὶ σύσσωμα καὶ συμμέτοχα τῆς ἐπαγγελίας ἐν Χριστῷ Ἰησοῦ διὰ τοῦ εὐαγγελίου,

εἶναι τὰ ἔθνη – The infinitive probably marks a content clause that defines ἀπεκαλύφθη. The clause defines the new status of τὰ ἔθνη, using a series of predicate nominative nouns.

συγκληρονόμα καὶ σύσσωμα καὶ συμμέτοχα – Predicate nominative adjectives which define the subject τὰ ἔθνη. Their similar construction forms alliteration and paronomasia. σύσσωμος means “belonging to the same body” and συμμέτοχος means “sharing in some possession or relationship.”

τῆς ἐπαγγελίας ἐν Χριστῷ Ἰησοῦ διὰ τοῦ εὐαγγελίου – The initial genitive describes the basis for this mutual involvement, i.e., the promises which are related to the Messiah Jesus (genitive of association; cf. 5:7). These promises in turn come “through the gospel/good news.” τῆς ἐπαγγελίας is modified by two adverbial prepositional phrases.

3.7  οὗ ἐγενήθην διάκονος κατὰ τὴν δωρεὰν τῆς χάριτος τοῦ θεοῦ τῆς δοθείσης μοι κατὰ τὴν ἐνέργειαν τῆς δυνάμεως αὐτοῦ.

οὗ ἐγενήθην διάκονος – Relative clause and the antecedent of the pronoun probably is τοῦ εὐαγγελίου, but it could also be Χριστῷ Ἰησοῦ. The genitive case marks the pronoun as a definer of διάκονος. The aorist passive verb indicates a completed action and defines some kind of change.

κατὰ τὴν δωρεὰν – Adverbial prepositional phrase indicating how (by what standard?) the subject has become “an assistant” of the gospel.  

τῆς χάριτος τοῦ θεοῦ τῆς δοθείσης μοι – τῆς χάριτος is the qualifier of δωρεὰν. This phrase reflects the phrase in v.2 and perhaps functions as something of an inclusion. τοῦ θεοῦ here probably is a subjective genitive as in v. 2. τῆς δοθείσης functions adjectivally, qualifying τῆς χάριτος. It is an aorist passive participle. Who is the assumed agent? It is modified by the indirect object μοι.

κατὰ τὴν ἐνέργειαν τῆς δυνάμεως αὐτοῦ  — An adverbial prepositional phrase which modifies the participle τῆς δοθείσης. The genitive τῆς δυνάμεως may be epexegetical or attributive. The genitive personal pronoun is probably subjective genitive.