If (a + b) : (a - b) = 15 : 1, then the value of a²– b² is 

Given $\frac{a+b}{a-b}=\frac{15}{1}$

Use Componendo and dividendo

$\begin{array}{rcl}\frac{a+b+a-b}{a+b-a+b}& =& \frac{15+1}{15-1}\\ \frac{2a}{2b}& =& \frac{16}{14}\\ \frac{a}{b}& =& \frac{8}{7}\end{array}$

Hence, $a^2-b^2=64-49=\boxed{\mathbf{15}}$