smc

Notice that the given equation, $(x^2-2xy+y^2{)}^7$ can be factored into $(x-y{)}^{14}={\sum }_{k=0}^{14}(\genfrac{}{}{0ex}{}{14}{k})(-1{)}^k\cdot x^{14-k}\cdot y^k$. Notice that if we plug in $x=y=1$, then we are simply left with the sum of the coefficients from each term. Therefore, the sum of the coefficients is $(1-1{)}^7=0,\boxed{0}$.