When Jesus said he lives because  of the living Father what do because(δια) and living Father mean at John 6:57?
57 As the living Father (ὁ ζῶν πατὴρ) sent me, and I live because of the Father (τὸν πατέρα); so he that eateth me, he also shall live because of me (American Standard Version)
In Greek the anaphoric article "τὸν" is inserted and serves to identify the second instance of "Father" as "the living Father." My question is not intended as a quotation of John 6:57 and emphasizes that the Son lives because of the living Father.
BDAG gives δια the sense of cause at J 6:57 and "an expression of divine action."
 BDAG δια w. acc
2. marker of someth. constituting cause
β. w. acc. of pers. and freq. as expr. of favorable divine action (Aristoph., Plut. 468; Dionys. Hal. 8, 33, 3, 1579 μέγας διὰ τ. θεούς ἐγενόμην; Ael. Aristid. 24, 1 K.=44 p. 824 D.: δι᾿ οὓς [= θεούς] ἐσώθην; SIG 1122; OGI 458, 40; PGM 13, 579 διῳκονομήθη τ. πάντα διὰ σέ; EpArist 292; Sir 15:11; 3 Macc 6:36: other exx. in SEitrem and AFridrichsen, E. christl. Amulett auf Pap. 1921, 24). ζῶ διὰ τὸν πατέρα J 6:57 (cp. PKöln VI, 245, 16 of Isis σὺ κυρεῖς τὰ πάντα, διὰ σὲ δ᾿ εἰσορῶ φαός ‘you are responsible for everything and thanks to you I can see light’). διὰ τὸν ὑποτάξαντα by the one who subjected it Ro 8:20.—DELG. M-M. TW