I cashed savings bonds in 2015, but did not record the original purchase date, nor do I know the gift date, as these were given to me when I was very young.

[CalCountry]

When you cash savings bonds, it is the accumulated interest earned that has not yet been reported which becomes taxable income to you.  You should have received a Form 1099-INT from the institution where you cashed the bonds.  The interest earned on U. S. savings bonds is reported in Box 3 of the Form 1099-INT.  The original purchase cost of the bonds, their purchase date, and the date of the gift are neither relevant nor needed.