Find n ∈ Z^+ such that 3^8 + 3^10 + 3^12 + 3^n is a square integer

Not sure if this the only natural number(positive integer) n that forces the exponential expression to be perfect square.
Taiwanese Cyh1368 and the modest Finnish mathematician Jyrki Lahtonen covered a base 2 three term expression similar to this problem. Factoring out the lowest power leads to a case by case discovery solution method.