You can translate this in a positive form. Possible meanings are that 1) Paul is not ashamed of believing the gospel because he knows it is true. Alternate translation: "I am confident in the gospel" 2) Paul is not ashamed of preaching the gospel because he knows that is true. Alternate translation: "I confidently preach the gospel"
Here "believes" means that one puts his trust in Christ. Alternate translation: "it is through the gospel that God powerfully saves those who put their trust in Christ" (See: [[rc://en/ta/man/jit/figs-explicit]])