There is actually a spot, the L2 Lagrange point, where something can orbit in a way where it's balanced from the sun's gravity and the earth's gravity, and as as a result anything orbiting there will continuously be in the earth's shadow.

That's where they put the James Webb space telescope, because being in the Earth's shadow means it can avoid interference by the sun and stay super cold, allowing it to take amazing readings of distant things.

Unfortunately, if you're out where the sun doesn't shine, your solar panels don't work very well, and for something as hungry as a datacenter, that's a problem.