he never did, it's from a novel

This one
it predates every non-fiction instance of the phrase being used to my knowledge

This phrase is from the novel "Children of the Arbat" (1987) by Anatoly Naumovich Rybakov (1911 - 1998). This is how J.V. Stalin speaks about the execution of military experts in Tsaritsyn in 1918: “Death solves all problems. There is no person, and there is no problem. Later, in his “Novel-Memoir” (1997), A. Rybakov himself wrote that he “may have heard this phrase from someone, perhaps he came up with it himself.” That was the Stalinist principle. I just, briefly formulated it.

from here