The maximum weight of the United States Postal Service's small flat-rate box is 70 pounds. Paul Sherman noticed that given that the box is only 75 cubic inches, "it is physically impossible to exceed the 70-pound domestic weight limit for a small flat rate box," even if you filled it with the heaviest element known to man.
Sherman writes that filled with osmium, the densest element, it would weigh 61.48 lbs. He points out that if you filled it with neutrons, however, it would exceed the USPS's weight limit and then some.
I figure that if you filled one with lead, it would weigh only 31 pounds. If you filled it with the sun (hydrogen and helium), you'd be ok so long as you got your sun from fairly close to the surface, but once you get deep into the sun the pressure goes up and you'd need more boxes. If you got 70 cubic inches of the sun from its core you'd need to spread it over a dozen or so boxes, but you'd also be needing to use some extra tape to hold in helium and hydrogen at 3.8 trillion psi.
