Kiuvera-Class Cutter: (1 core) Middle of the spine, between the two raised panels.
Sunat-Class Corvette: (1 core) Middle of the body
Periat-Class Frigate: (2 cores) Middle of the body; Middle of the tail, below the bridge.
Malrak-Class Carrier: (2 cores) Middle of the body above the hangar; Middle of the tail below the bridge.
Imerat-Class Destroyer: (3 cores) Middle of the body beneath the big cannon; One in each wing of the body, where the white overlay plates meet.
Kythera-Class Battlecruiser: (4 cores) Center of the body, above the Fusion Reactor; At the rear, below the Bridge; Mid-rear, below the Warp Drive; I think the last one is below the combat bridge in the nose?
Kamirat-Class Battlecarrier: (4 cores) Same layout as the Kythera.
Tovera-Class Dreadnought: (5 cores) Three of the cores are centerline from bow to stern on different decks, spaced roughly evenly apart; The last two cores are in the wings around 1/3 of the way from the main body.

Unless you're using a dedicated combat CV designed to take out cores; you're better off taking out the rear thrusters of the ship to force it to stop; clearing a safe approach vector and then boarding it to get the cores on foot.
All RE2 OPV cores are accessible on foot.

Wow thank you soo much!

Originally posted by Vermillion:

Kiuvera-Class Cutter: (1 core) Middle of the spine, between the two raised panels.
Sunat-Class Corvette: (1 core) Middle of the body
Periat-Class Frigate: (2 cores) Middle of the body; Middle of the tail, below the bridge.
Malrak-Class Carrier: (2 cores) Middle of the body above the hangar; Middle of the tail below the bridge.
Imerat-Class Destroyer: (3 cores) Middle of the body beneath the big cannon; One in each wing of the body, where the white overlay plates meet.
Kythera-Class Battlecruiser: (4 cores) Center of the body, above the Fusion Reactor; At the rear, below the Bridge; Mid-rear, below the Warp Drive; I think the last one is below the combat bridge in the nose?
Kamirat-Class Battlecarrier: (4 cores) Same layout as the Kythera.
Tovera-Class Dreadnought: (5 cores) Three of the cores are centerline from bow to stern on different decks, spaced roughly evenly apart; The last two cores are in the wings around 1/3 of the way from the main body.

Unless you're using a dedicated combat CV designed to take out cores; you're better off taking out the rear thrusters of the ship to force it to stop; clearing a safe approach vector and then boarding it to get the cores on foot.
All RE2 OPV cores are accessible on foot.

What weapon will destroy cores on the ships? do i use charged explosives?

If you're on foot, any weapon will destroy the core if you're able to see it, just like any regular POI core.
If you're in a ship, if it goes "boom" then it can probably destroy a core.
Basically, if it's a weapon, it can destroy a core.