Is hypocalcemia related to gout?

Not usually related. Gout is related to high uric acid levels causing joint pains and swellings. Low calcium is usually due to kidney disease, parathyroid disease, or medications, among others. In acute (sudden) kidney failure from uric acid stones, low calcium can happen, but this would be an uncommon situation. A rare condition called tumor lysis syndrome can also show low calcium and high uric acid levels.
Gout. Is elevated uric acid or hyperuricemia in the blood. (though not all hyperuricemia causes gout).