I researched it a little, and wrote about it previously: https://jungdongha.blogspot.com/2017/03/tbt-2-whale-hunt-immortal-song2-july.html
From the audience reaction, and seeing how people are enjoying it and mouthing the lyrics, it's obvious that this song is very well known. Well, so are almost all other songs performed on this TV program. Koreans cherish their songs.
-- "Whale Hunt" --
( 고래 사냥, Chung Dong-Ha & DickPunks )
No matter how I drink, sing and dance
My heart's still full of only sadness
I search for a cause to give myself to
But everything has its back turned on me
Now let's all set out for the East Sea
Riding on a third class slow train
The world in the dream I had last night
It's forgotten as I wake up in the morning
Yet I got a dream that stays in my mind
The one about a beautiful little whale
Now let's all set out for the East Sea
To catch that whale breathing a myth
Even if our love crumbles to pieces
Even if we lose everything overnight
We still have it vividly in our mind
We have this beautiful whale