Παῦλος ἀπόστολος, οὐκ ἀπ’ ἀνθρώπων οὐδὲ δι’ ἀνθρώπου ἀλλὰ διὰ Ἰησοῦ Χριστοῦ καὶ Θεοῦ Πατρὸς τοῦ ἐγείραντος αὐτὸν ἐκ νεκρῶν,
Most translations render [ bold] above as "God the Father." For example,
New International Version
Paul, an apostle--sent not from men nor by a man, but by Jesus Christ and God the Father, who raised him from the dead--
However this is an ungrammatical translation since the bold English expression above ("God the Father") is one of essential predication (i.e. God the Father, God the Son, God the Holy Spirit) rather than of identity (i.e. God = Father).
Yet the expression Θεοῦ Πατρὸς is one where we have two nouns in simple apposition. In other words this construction indicates an identical exchange between both nouns. The mathematical formulas of A=B, B=A are thus applicable in this instance. To put it in another way, Θεοῦ is not predicating or attributing something to Πατρὸς but rather it is identifying him as such. So the correct translation is as follows:
Paul, that is, the apostle --sent not from men nor by a man, but by Jesus Christ and by God, that is, the Father who raised him from the dead--
In this regard Darby Bible Translation comes closest to an accurate translation by bracketing the article "the".
Paul, apostle, not from men nor through man, but through Jesus Christ, and God [the] Father who raised him from among [the] dead,