The Greek aitios (αἴτιος) means responsible for, or the one accountable. As a noun it refers to the guilty party or the one who bears responsibility. In legal contexts it denotes the one against whom a charge is laid.
Pilate found no cause of death in Jesus (Luke 23:4) — the sinless one was without legal guilt, yet He bore ours. Hebrews calls Him the source (aitios) of eternal salvation (5:9). Christ is the ultimate Cause: innocent of sin, yet causally responsible for the salvation of all who obey Him.