The following are a list of subjects or topic that Jesus Christ mentioned during His 3 1/2 years of His ministry. I listed the topic and the number of times they are mentioned throughout the four gospels of Matthew, Mark, Luke and John by Jesus Christ.
The Kingdom of God (Heaven) : total 90
Love: total 67
God ( or Father in heaven) : total 52
Prayer (Pray) : total 39
Sabbath : total 18
Baptize (Baptism) : total 15
Worship (worshipped) : total 12
Righteousness : total 7
Resurrection : total 7
Tithe (Tithing or Tithed) : total 3
Redeemed ( redemption) . total 1
And what is surprising is ALL 10 Commandment of the Old Covenant are never mention by Jesus Christ within the four gospels
So to answer your question, I would say the core of Jesus Teachings was the Kingdom of God.