1 Corinthians 10:16 The cup of blessing which we bless, is it not the communion of the blood of Christ? The bread which we break, is it not the communion of the body of Christ?

10:17 For we being many are one bread, and one body: for we are all partakers of that one bread.

Paul is referring to the Lord's supper. The Lord's supper is not the passover meal Christ eat with the twelve, nor is it to commemorate the new testament.

The cup of blessing is the cup the church, the body, blesses for the blood of Jesus shed for our justification unto eternal life. It is the communion of his shed blood, that the body, the church, shares together with the Lord Jesus Christ and with the members of his body, the church.

Paul is saying, just as Jesus broke bread at the passover meal, we have a bread that we also break, and that is the bread of communion with the members of the body, the church of God.

1 Corinthians 10:20 But I say, that the things which the Gentiles sacrifice, they sacrifice to devils, and not to God: and I would not that ye should have fellowship with devils.

10:21 Ye cannot drink the cup of the Lord, and the cup of devils: ye cannot be partakers of the Lord's table, and of the table of devils.

Paul was admonishing the Church to flee from idolatry. The Church is one with Christ, and is one body. In light of being spiritual partakers of the Lord's table, where we partake of the communion of his blood, and bodily sacrifice, we can not also partake of the table of devils, by partaking in sacrifices offered to them.

Ephesians 2:16 And that he might reconcile both unto God in one body by the cross, having slain the enmity thereby:

Believers in Christ, Jew and Gentile, are one in Christ by his cross. Both are reconciled to God and the middle wall of partition between Jew and Gentile is removed (Ephesians 2:14