Are Mark 10:38 and Romans 6:3-4 not essentially two sides of the same coin?

Question

In the Gospel of Mark, Jesus responds to a request by James and John:

Mark 10:38: "But Jesus said to them, 'You do not know what you are asking. Are you able to drink the cup that I drink, or to be baptized with the baptism with which I am baptized?'”

There seem to be (at least) two elements Jesus is referring to:

1. The "cup" that He will drink might symbolize the beatings/scourging He would experience.
2. The "baptism" in this context appears to be the crucifixion itself (or the totality of events).

Similar language to Christ's impending ordeal appears in the Gospel of Luke:

Luke 12:50: "But I have a baptism to undergo, and how distressed I am until it is accomplished!"

Is this interpretation of Mark 10:38 correct? And, is this verse not essentially conveying the same thing we read in Paul's Letter to the Romans?

Romans 6:3-4: "Or do you not know that as many of us as were baptized into Christ Jesus were baptized into His death? Therefore we were buried with Him through baptism into death, that just as Christ was raised from the dead by the glory of the Father, even so we also should walk in newness of life."

Answer 1

Mark 10:

38 “You don’t know what you are asking,” Jesus said. “Can you drink the cup I drink or be baptized with the baptism I am baptized with?”

Referring to the coming suffering of the cross, I think Jesus expected that James and John to admit defeat and say no. But the brothers missed Jesus' point and replied:

39“We can,” they answered.

Instead of correcting the brothers' misunderstanding, Jesus graciously softened his position:

Jesus said to them, “You will drink the cup I drink and be baptized with the baptism I am baptized with,

Now, the baptism refers to the brothers' future martyrdoms in the name of Christ. As the OP pointed out, this passage is essentially confirmed by Paul in Romans 6:3-4:

"Or do you not know that as many of us as were baptized into Christ Jesus were baptized into His death? Therefore we were buried with Him through baptism into death, that just as Christ was raised from the dead by the glory of the Father, even so we also should walk in newness of life."

Indeed, James and John in their martyrdoms were baptized into Christ's death.

Are Mark 10:38 and Romans 6:3-4 not essentially two sides of the same coin?

Yes, essentially.