Cultivating Cores

Currently, Ban has a total of ten Cores, including the two Normal Grade E-Elite Rank Monster Cores he got from that Monsters of that two fellow who tried to rob him before.

Just like what Kuys said before, every Monster has their own Monster Cores regardless of Rank and Grade. The Summoner will need to strengthen this Monster Core for their Monsters to Rank Up. The methods range from letting the Monster eat beneficial foods for them all the way to using Methods that allow their Monsters to absorb Beast Cores. 

However, unlike Beast Cores, Monster Cores were naturally smaller. It might also be due to the fact that Monster Summons are smaller compared to Beasts of the same type with the same Rank and Grade.

And as such, the Monster Core that he got from the two Normal Grade E-Elite Rank Monsters were only the size of a fist, while the Normal Grade E-Elite Rank Beast Cores that he bought from the Blackmarket was about the size of two fists being combined.