(a+b)(a-b)=r^3

a+b=r^2

a-b=r

2a=r+r^2

a=(r+r^2)/2=r(r+1)/2

2b=r^2-r

b=(r^2-r)/2=r(r-1)/2

thus a=r(r+1)/2 and b=r(r-1)/2 work because for all integers r either r or r+1 is even and likewise either r or r-1 is even and thus these values for a,b are also integers.