Solomon secured his kingdom by executing his rivals (see 1 Kings 2). The three enemies he had put to death were old enemies of his father King David.
In a related way, Jesus also established His kingdom by bloodshed. But it wasn't someone else's blood that He shed, it was His own blood that He offered.
Also, note the three enemies Solomon had put to death are in many ways symbolic of the flesh, the world, and the devil. Jesus gives us victory over these old enemies through the power of the cross.