It is given that \(\mathrm{f}(n)=3^{3 n}+6^{n-1}\).
(i) Show that \(\mathrm{f}(n+1)+\mathrm{f}(n)=28\left(3^{3 n}\right)+7\left(6^{n-1}\right)\).
(ii) Hence, or otherwise, prove by mathematical induction that \(\mathrm{f}(n)\) is divisible by 7 for every positive integer \(n\).