Lucemon
Lucemon is a Wizard Digimon that you earn when you "digivolve" an Angemon or a Devimon. It's possible for you to obtain a Lucemon directly if you breed two Dark Digimons at level 75 or greater. One of Lucemon's attacks is called "Ultimate Sacrifice." During this attack, a Magic Square appears on the screen. The attack has a one-in-two chance of defeating enemies instantly. If it does not defeat them, it will damage them greatly. You can digivolve Lucemon into Daemon, but it will lose its Ultimate Sacrifice attack with the Magic Square.
BishopChessmon
The other Digimon that produces a Magic Square during one of its attacks is the Puppet Digimon BishopChessmon. Digivolve a KnightChessmon and you will get a BishopChessmon. You cannot produce a BishopChessmon through breeding. BishopChessmon's attack "Bishop Cross" produces a Magic Square. When you use this attack, you will destroy an enemy instantly. Should you choose to digivolve BishopChessmon further into KingChessmon, it will no longer have its Bishop Cross attack, so you will no longer see the Magic Square in action.
In the Game
In both examples, the Magic Squares are associated with attacks that have the power to instantly destroy enemies. A Magic Square in the game is the same as a Magic Square in mathematics, a square that features rows and columns of numbers. Each row, column and diagonal row of numbers add up to the same sum. You do not need to know how to solve the Magic Squares that appear on screen to play. If you took the time to add up the numbers in each column, row and diagonal, you would see that they add up to the same sum.
Magic Square Benefits
Although the Magic Square attacks appear in the game only rarely, it's to your benefit to get Lucemon and BishopChessmon on your team so that you can have access to Magic Square attacks. The power to instantly destroy enemies, even if in Lucemon's case, it's a one-in-two chance, can help you get through battles quickly while still earning experience points in order to level up. Refrain from further digivolving at least one of these two Digimon so that you can retain the Magic Square attack to use when you want to earn experience points quickly.