In all honesty though I don't know that anything we could do in a conventional sense would have any effect. We can't even get at our own core, let alone get another planets core going. There is still so much we don't know, both about our own inner workings, and about the geology of Mars. We can make educated guesses, but I think we will be stuck with more questions than answers until we get a team of geologists on the Martian surface to do the kind of surveying it took for us to figure out our own geology and history of the earth.

Outside of mainstream thinking, there are radical ideas that might work and it's not science fiction. It's doable but we wouldn't reap the rewards in human time scales.

You could nudge comets and asteroids out of their orbits to collide with Mars. Comets would bring back the gasses to replenish the atmosphere allowing liquid water (but no oxygen), and if you did something like crash a protoplanet like Ceres into Mars, it would destroy both bodies but they would go molten and fuse into a new larger planet. Since many asteroids are metal rich, it's possible in theory you could bombard enough of them to give the new planet a liquid core that would last awhile. The only problem is it would be a ball of fire for millions of years. So we probably won't do that.

The comet idea bears some merit though. Without a magnetosphere the atmosphere would disappear again, but it takes a very long time. And there are a lot of trans-Plutonian bodies to nudge out of orbit to keep replenishing it.

I think if we were going to colonize something the moon would make more sense though. Mars really doesn't have anything we need for life, to offer us except gravity. The moon is made from similar rocks as the earth, and trying to terraform the moon would be a lot easier than terraforming a planet. It would also be closer, just a 3 week trip with traditional rockets, only a 2 second radio delay to the ground, and it's closer to the sun than Mars allowing plant growth even better than the Earth without all that atmosphere scattering the sunlight.