A.T. Robertson Commentary Mark 8:31

"And he began to teach them, that the Son of man must suffer many things, and be rejected by the elders, and the chief priests, and the scribes, and be killed, and after three days rise again." — Mark 8:31 (ASV)

He began to teach them (ηρξατο διδασκειν αυτους). Mark is fond of this idiom, but it is not a mere rhetorical device. Matthew 16:21 expressly says "from that time." They had to be told soon about the approaching death of Jesus. The confession of faith in Jesus indicated that it was a good time to begin. Death at the hands of the Sanhedrin (elders, chief priests, and scribes) in which Pharisees and Sadducees had about equal strength. The resurrection on the third day is mentioned, but it made no impression on their minds. This rainbow on the cloud was not seen.

After three days (μετα τρεις ημερας). Matthew 16:21 has "the third day" (τη τριτη ημερα) in the locative case of point of time . There are some people who stickle for a strict interpretation of "after three days" which would be "on the fourth day," not "on the third day." Evidently Mark's phrase here has the same sense as that in Matthew and Luke else they are hopelessly contradictory. In popular language "after three days" can and often does mean "on the third day," but the fourth day is impossible.