Numeric mana symbols (, , and so on) in mana costs of permanents you control don’t count toward your devotion to any color.

Mana symbols in the text boxes of permanents you control don’t count toward your devotion to any color.

Hybrid mana symbols, monocolored hybrid mana symbols, and Phyrexian mana symbols do count toward your devotion to their color(s).

Your devotion to black is calculated when you determine Marshmist Titan’s total cost, and that cost is locked in before any costs are paid. For example, if you control a creature with black mana symbols in its mana cost that can be sacrificed for mana, those mana symbols will count toward your devotion to black. You can then sacrifice that creature for mana to pay the reduced total cost.

If your devotion to black is greater than six, Marshmist Titan will cost to cast. The colored mana requirement isn’t reduced.