If you're specifically curious about Solzhenitsyn's figure, you might want to check out this answer I wrote about where he got them.

A brief summary from that answer - Solzhenitsyn cites extremely high numbers of "victims of communism" (so not exactly the same as gulag deaths) based off of information from the statistician Ivan Kurganov. Kurganov had quite the wild history: he fought for the Whites in the Russian Civil War, became a statistician for the Soviets in 1920s, then collaborated with the Germans in World War II and relocated to Berlin, then emigrated to New York after the war. His figures are and were even at the time considered extremely dubious (other Soviet emigres requested that Solzhenitsyn stop citing Kurganov), and are based off of population projections rather than documentation of deaths (so basically Kurganov was arguing that the Soviet population should have been 66 million/110 million higher without Soviet rule).

The most charitable interpretation of Solzhenitsyn making these claims is that he was trying to force the Soviet government to release its records to disprove his claims. The less charitable interpretation is that he gave a platform and wide currency for a bunk statistic created by a Nazi collaborator.

With that said - the Gulag records are considered to underreport camp-related deaths. Part of this was padding figures by releasing terminally sick prisoners before they died. There is some debate as to what the true figure should be - one academic historian, Golfo Alexopoulos, claims about 6 million related deaths, but most historians put the total death range around 1.5-1.7 million. Historian Timothy Snyder gives a total Soviet death count under Stalin (including famine victims) up to 9 million, but other historic estimates that have made since about 1990 for total deaths under Stalin can go up to 20 million.