Suggested translations:
John 16:27-28: "...for the Father Himself loves you, because you have loved Me and have believed that I came from the Father."
John 8:42" "...Jesus said to them, “If God were your Father, you would love Me, for I was born from God and I come, thus I have not even come on My own initiative but He sent Me."
The rationale for these translations occur from the parallels to the LXX, which are remarkable. For example, the exact Greek phrase "παρὰ τοῦ θεοῦ" ("from God") occurs fourteen times in the LXX, and the LXX translations are as follows:
Gen 41:32 - ...the matter that is from God...
Ex 4:20 - ...[Moses] took the rod from God...
Ex 14:13 - ...see the deliverance from God...
Ex 18:15 - ...to seek judgment from God...
Judg 9:13 - ...the good cheer of men which comes from God...
1 Chr 5:22 - ...because the war was from God...
2 Chr 10:15 - ...because it was a reversal from God...
2 Chr 22:7 - ...and from God came ruin...
Neh 8:23 - ...and we sought from our God...
Neh 16:16 - ...with the help of our God...
Ps 7:11 - ...righteous is my help from God...
Ps 103:21 - ...to seek their food from God...
Is 13:6 - ...destruction will come from God...
Is 52:10 - ...the salvation that comes from God...
From these examples, one can infer that the LXX uses to Greek phrase "παρὰ τοῦ θεοῦ" to indicate the agent by whom something is sent. In other words, in the Gospel accounts, when Jesus uses the phrase "παρὰ τοῦ θεοῦ [ἐξῆλθον]" in reference to himself, he is indicating that God sent him.
The phrase, "ἐκ τοῦ θεοῦ," however, does not occur in the LXX. In 392 places, however, the genitive phrase "ἐκ τοῦ" does occur, but in most cases, the object of the prepositional phrase is an IMPERSONAL object (inanimate). For example, "out from heaven" (Judg 5:20) or "out from the river" (Gen 41:18). The idea is locative somewhere; that is, something comes out of heaven, or the river.
There are five exceptions in the LXX, however, that refer to PEOPLE (non-inanimate), and the verses are as follows:
Gen 19:32, 34-37 (LXX Translation)
32 Come, and let us give our father wine to drink, and let us lie with him and raise up offspring from our father.” 34 And it came about on the next day that then the elder said to the younger, “Look, I lay yesterday with our father; let us give him wine to drink this night also, and when you have gone in, lie with him, and let us raise up offspring from our father.” 35 And they gave their father wine to drink on that night also, and the younger, when she had gone in, lay with her father, and he did not know when she lay down and got up. 36 And the two daughters of Lot became pregnant by their father. 37 And the elder bore a son and called his name Moab: “From my father”; he is the ancestor of the Moabites to the present day.
The fifth place in the LXX where the object of the prepositional phrase is PERSONAL (non-inanimate) is the following verse:
Gen 38:25 (LXX Translation)
32 But as she was being brought she sent to her father-in-law, saying, “By the man whose things these are, I am with child.” And she said, “Take note whose is the ring and the small necklace and this staff.”
In other words, Tamar was indicating that Judah was the father of her unborn child.
In summary, when one reads the Christian New Testament through the lens of the LXX (in the Greek language), there are interesting nuances that appear. For example, when Jesus uses the phrase "παρὰ τοῦ θεοῦ [ἐξῆλθον]" in reference to himself in John 16:27-28, he is indicating that God sent him. However, when in reference to himself he then uses the phrase "ἐκ τοῦ θεοῦ [ἐξῆλθον]" in John 8:42, he is indicating that he was born from God. Please note that this verse captures both the "birth" and "sent" aspects!