Per Help for "Excel specifications and limits", the "largest number
allowed to be typed into a cell" is 9.99999999999999E307 and the
"largest allowed positive number" (resulting from a formula) is
1.79769313486231E308. The latter limit is specified by the IEEE 754
standard for double precision numbers.
If you don't need to do math with these numbers, you can prefix with a
single quote to force it to be text.
If you do need to do math with such large numbers, you might look at the
xlPrecision Add-In from http://precisioncalc.com/