First things first. The case dimensions should be inches, not feet. If they were feet you would be able to get many thousands of bottles in the case, not just 24.
So I'll assume the dimensions are inches. The cases can be laid in three different ways, so for starters we'll calculate by their length, 15.1 inches.
Number of cases fitting around the earth if they're packed end to end: 24901*5280*12/15.1=1.04485*10^8.
Therefore 2.6*10^9 cases would girdle the earth 2.6*10^9/1.04485*10^8=24.88 times.
If the cases are side by side (8.3in apart) this changes to 24.88*8.3/15.1=13.8 times; and if 10.2in apart=16.81 times, because more cases can girdle the earth if packed differently.
The volume of one case is 15.1*10.2*8.3=1,278.366 cu in=0.74 cu ft. 1.04485*10^8*1278.366=total volume of cases placed lengthwise=7.76*10^7 cu ft.