Nit: The energy of an object going 2,000 m/s is 1/16th of that going 8,000 m/s, but since this is a rocket launching from Earth the energy for the rocket to get to 2,000 m/s is much greater than the energy to go from 2,000 m/s to 8,000 m/s [1].
Just look at how much larger the first stage (mass almost all propellant) is compared to the second stage (large fraction of the mass is the payload).
Just look at how much larger the first stage (mass almost all propellant) is compared to the second stage (large fraction of the mass is the payload).
[1] https://en.wikipedia.org/wiki/Tsiolkovsky_rocket_equation