Interesting...I had the exact OPPOSITE problem!
I spent seven years in ATC, where we use ICAO for all airports, so Heathrow was always "EGLL", Gatwick "EGKK" and so on.
Now I am flying, and like every airline we use IATA codes. So it confused me at first to see "LGW"..."GW" would get me thinking of "EGGW" and therefore Luton! "HAJ" for Hanover? "EDDV" is surely more intuitive! And so on.
There is a logic to ICAO...The first letter is the region, followed by country code, followed to two letters for the airport.
"EG.." Europe, Great Britain
"ED.." Europe, Germany
"LF.." Europe, France
"K..." USA
Some IATA codes are obvious...like JFK, STN, AMS, but TXL for Berlin? FCO for Rome?
Each system has it's pluses and minuses - but you have 456976 ICAO codes to 17576 IATA codes.
A prize to the first person to list them all....