This could be The Last Legionary series, written by Canadian author Douglas Hill. The main four-volume series (Galactic Warlord, Deathwing Over Veynaa, Day of the Starwind, and Planet of the Warlord) was published from 1979 to 1981 (with a much lower quality prequel, Young Legionary in 1982).
The series is a classic of space opera for children. The protagonist—the eponymous last Legionary, Kiell Randor—travels from planet to planet, battling agents of the titular Warlord, who is slowly plotting to take over the galaxy. The galaxy in the series is actually our own, but there the home planet of Earth is not mentioned anywhere, human civilization having spread all across the stars through the use of Overlight travel.
In Galactic Warlord, the entire population of Kiell's home planet of Moros is wiped out by a radiation bomb, planted by members of Deathwing, the Warlord's group of elite agents. The people who had originally colonized Moros, which was practically a death world, had grown to become extremely tough or resilient, and they eventually formed the galaxy's most elite mercenary corps, the Legions of Moros, who posed an obvious danger to the Warlord's plans. Kiell, whose battle group was away from Moros at the time of the attack, receives only a limited dose of the deadly radiation when he returns to Moros's star system—enough to kill him, but only slowly.
As he searches for more survivors, as well as information about who killed his people, Kiell is kidnapped by a group of reclusive scientists who have also come to realize the danger the Warlord poses, although they still know very little about the Warlord; the Warlord's actual identity is unknown until the fourth book, and the Warlord's long-term plans for galactic domination are only inferred. The scientists, with the help of a flying, telepathic, extragalactic alien named Glyr, kidnap Kiel and completely replace his irradiated bones with a synthetic skeleton—saving his life and giving him a skeleton that is effectively unbreakable under normal circumstances. As he heals, they brief him about what they do know about the Warlord, then dispatch him and the alien Glyr to investigate and try to thwart the Warlord's future endeavors.
The third book, Day of the Starwind, specifically features of tower as an important thematic element, and the tower was shown on most versions of the book cover. If you read the books in the early to mid-1980s in hardback, you may well have seen the original cover, the first one shown below.
(What is the Millennium Falcon doing on this one?)
There is also one more commonly seen cover, which I have not posted, because it does not obviously show the Deathwing tower, and it actually shows a major spoiler.
Day of the Starwind and Planet of the Warlord (but not seemingly the first two books) can be checked out for free from archive.org.
The Last Legionary books have also be a frequent target for story-identification questions:
