因為…所以… links two full clauses, cause then drawn-out effect. 因為…的關係 compresses the cause into a noun ('owing to X') and lets the result follow on its own; 所以 is optional, not the partner.
由於 is the formal cause-marker that opens a clause on its own. 因為…的關係 specifically nominalizes the cause with 的關係, naming a circumstance rather than narrating it.
因為下雨的關係所以不能去。 ✗ → 因為下雨的關係,不能去。 ✓ (the boxed cause already carries the link; 所以 is redundant)
因為他遲到了的關係。 ✗ → 因為他遲到的關係。 ✓ (的關係 wraps a noun-like cause; drop the clause-final 了)
工作的關係,他常加班。 ✗ → 因為工作的關係,他常加班。 ✓ (keep 因為 to open the box)
English 'because of X' maps cleanly, but learners often append 'so' (所以) the way English allows 'because…, so…'; here the noun-packaged cause makes 所以 unnecessary.