When casting Thanos, the Mad Titan with commander tax, does the colorless mana paid for the tax reduce the power-up cost during that turn?

[[Thanos, the Mad Titan]]

I understand that a creature's power up cost is reduced by the mana spent to cast it IF you are powering it up during the turn it is put in play. However, if you pay a colorless mana to cast Thanos with commander tax, does that reduce the colorless mana cost to activate his power-up ability?

If a blue mana is used to pay for the commander tax, does that discount the blue mana required for the power up?

Thank you!