Show that $2^n+1\mid 8^n+1$ I tried by induction but at induction step I struck.I am bad at proving statements which involve variables as exponents.I gladly appreciate any help

Use modular arithmetic: $2^n\equiv -1 \mod 2^n+1$,

so $8^n=2^{3n}=(2^n)^3\equiv(-1)^3=-1\mod 2^n+1$