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Boxing legend Leon Spinks is battling prostate cancer that spread to his bladder -- but the family is hopeful he'll pull through.

TMZ Sports broke the story ... 66-year-old Spinks has been fighting for his life in a Las Vegas hospital.

Now, a family spokesperson is revealing more details about Leon's condition.

"Leon is currently in intensive care of a Las Vegas hospital receiving attentive medical care to suppress prostate cancer which he was diagnosed with earlier this year and has since spread to his bladder."

"The last few months have been an agonizing roller coaster for Leon and his wife, Brenda, with continuous hospital stays."

"Leon is showing small signs of improvement and progress. A miraculous fighter his entire life, we are optimistic and hopeful that he will move out of ICU soon."

"The power of prayer is real and his family is beyond grateful for all of the tremendous love and support."