Mistakes happen, and the reviewers and editor know this. However, you are probably right that they will have less trust for your results once they see there was a major mistake. Once these particular people have confirmation that the calculation had been wrong, it's possible they may not want to spend more effort on this paper, but if that is the case they would probably return a negative result quite quickly. That would free you to submit the improved paper to another journal.
Let's assume your calculation mistake was truly huge, but that you still have workable results after fixing it. How might the reviewers and editor react to learning this, and how can you address their concerns?
Overall, they might worry about whether the other results are accurate.
Before resubmitting, make sure that you catch all of the mistakes possible. Ask trusted colleagues to "sanity check" everything with you, including asking some the big favor of doing an in-depth check of all your calculations, to make sure that you uncover any other potential errors.
If there are additional tests you can perform (specification checks, testing how strong your results are to the omission of outliers, etc.) it may be appropriate to include these in a new appendix. These could reassure the reviewers about the integrity of your approach, the underlying data, and how you're handling it. This would also give them more chances to spot inconsistencies--which would hopefully not be present. (If such checks show that your results may not be robust, you may want to acknowledge that as a new limitation in the paper--honesty and transparency will matter to the reviewers.)
Emphasize in the cover letter that you have fully rechecked all of the calculations, after sincerely thanking the reviewer for pointing out the problem and acknowledging that you had to make a major revision. (It may be appropriate to address how the mistake came about and the steps you have taken to check and cross-check the remaining calculations.)
Make sure you are as detail-oriented as possible with this draft, including by dealing thoroughly with unrelated problems. If you can hire someone to copy-edit the submission, this would be a good time. Even small errors in other places may be seen by these reviewers as a bad sign.
Allow them to verify your results, if at all possible. Clean up your programs/calculations while reviewing, such that you can share them. If the programs are long or complicated, provide an overview document explaining the structure. This is far more than what you might publish as an appendix, but you want the reviewers to be able to check the process step by step.
Is it possible to share your raw data (e.g. without violating confidentiality or breaking anonymity of review or earning the ire of colleagues who want to keep the data private)? If so, that should be part of what you share, so they can replicate your analysis if interested. (It may be beyond their scope of duty to go this in-depth, but you should make it easy for them to do so if they want to.)
If there is no established way in the publishing management system to share these additional files, you should state in your cover letter your willingness to share the full data and calculations and ask the editor whether there is an established procedure for this.
The reviewers may have initially been interested in the paper, and granted the revision, because of the result that referee considers unexpected. I'm not entirely sure from the question whether you still have this unexpected result after performing your major revision.
If there was a change in the meaning of your results, be sure to edit the "frame" for your results (in the abstract, introduction, discussion, and/or conclusion, especially). I.e., if nothing changes beyond the "Analysis" and "Results" section, then this would be a problem.
Make sure you acknowledge the previous findings that the reviewer pointed out. If your revised results are still "unexpected," then make sure that the discussion addresses and conjectures about the discrepancy in productive ways.
If there are other reasons for skepticism around that result that the reviewer provided, you may want to come up with specific ways to test them, and include the results in either a "falsification check" section or an appendix.
Your (eventually) published paper should include sincere acknowledgements to any colleague(s) who helped and the anonymous reviewers who helped you strengthen the work.