What the NT presents, differs considerably from what the Didache presents.
Commentary from Harvard Professor, Helmut Koester:
"The Eucharist prayers [in the Didache] also have their origin in Hellenistic Judaism. ... In their Christian form they relate the cup to the covenant of David and understand the bread as the symbol of the oneness of the congregation. There is no attempt to connect wine and bread... to the death of Jesus .
[T]here is no reason to assume that the communities of Syria, for whom the Didache was written, followed the same eucharistic practice and formulae that are attested in 1 Cor 11:23- 26. [This is my body, this is my blood, etc.] Rather, these prayers may well belong to a direct continuation of the fellowship meal that Jesus celebrated with his disciples and friends."
[Koester, Helmut. History and Literature of Early Christianity, Volume 2, Introduction to the New Testament, 2d edition. (2000), pg. 164]
This is your source so find in the bible the covenant of David and find how it relates to the Cup of the covenant of david.