The answer is in your heart

Given = $\frac{[x+y]^{2} - 1}{5} = 14^{3}$ and $x^{2} + y^{2} = 111^{2}$

$\huge = x^{2}+y^{2}+2xy-1 = \huge5[14^{3}]$

$\huge xy = \frac{5[14^{3}] - 111^{2} + 1}{2}$

By solving this we get the answer as $\huge700$