You lost 6 orders of magnitude to this IMHO:

5610 million km^3 = 5.61 * 10^3 * 10^6 km^3 = 5.61 * 10^9 km^3 = 5.61 * 10^9 * 10^9 m^3 = 5.61 * 10^18 m^3

But you said the resulting volume was = 5.61 * 10^12 m^3.

I think you forgot that it was 5610 million km^3.