A planetary core or simply core is the innermost layer at the center of a planet or an asteroid. In the same way that a stellar core was the center of a star.
M-class planets had a nickel-iron core. (TNG: "Clues")
In 2258 of an alternate reality, Nero used a mining drill on the Narada to dig to the core of Vulcan. He then put red matter into the core of Vulcan creating a black hole and destroying the planet. (Star Trek)
The planet Terra 10 had a molten core surrounded by a mantle and crust that was entirely crystalline. (TAS: "The Terratin Incident")
The gas giant Tethys III had a frozen helium core. (TNG: "Clues")
In 2368, an asteroid which threatened Tessen III with planetwide destruction had a core of nitrium and chrondite. (TNG: "Cost of Living")
The moon Jeraddo around Bajor had a molten core, and in 2369, there were plans to transfer energy from this core, forcing the evacuation of the residents. (DS9: "Progress")