This cup was probably the third cup drunk in the Passover meal, namely, the "cup of blessing." It contained wine diluted with water. This diluted wine was what the Jews usually drank with their meals.  Jesus then gave thanks again. The Greek word eucharistesas ("gave thanks") is a cognate of euchariste ("thanksgiving") from which we get the English word "Eucharist," another name for the Lord"s Supper. [source][source][source]
Jesus commanded all of His disciples to drink from the cup. They had to personally appropriate what symbolized His blood as they had to personally appropriate what symbolized His body. Together these elements represented Jesus Himself. The Eleven learned to appreciate the larger significance of these things after His resurrection (cf. 1 Corinthians 11:23-28). [source][source][source]
Matthew 26:26-35 - A Self-Confident Disciple Warned
The Passover looked back to the dread hour of the Exodus; the Supper links Calvary with the Second Advent. In partaking of it we should not confine ourselves to either retrospect or anticipation, but should endeavor to feed our souls with the very spirit and heart of our dear Lord, so as to absorb His divine strength, sweetness and love. We need to feed on His flesh and drink of His blood after a mystical fashion, so that He may become the Life of our life. The word new is not the same as in Matthew 9:17, but contrasts, with the present order of things, something entirely different. The former things will have passed away-such was our Lord's anticipation!
The new covenant is further explained in Hebrews 8:1-13. It is good to recite its provisions when we sit at the Table. It is as though God and the believer drink of the cup in pledge of that blessed understanding between them. See how our Shepherd eagerly warns one of the sheep that was dear to Him and for which He had pleaded often, Luke 22:31. [source]
Chapter Summary: Matthew 26
1Jesus foretells his own death 3The rulers conspire against him 6The woman anoints his feet 14Judas bargains to betray him 17Jesus eats the Passover; 26institutes his holy supper; 30foretells the desertion of his disciples, and Peter's denial; 36prays in the garden; 47and being betrayed by a kiss, 57is carried to Caiaphas, 69and denied by Peter
What do the individual words in Matthew 26:27 mean?
Andhaving takena cuphaving given thanksHe gave [it]to themsayingDrinkofitall of you