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In this paper, we use lax monoidal TQFTs as an effective computational methodfor motivic classes of representation varieties. In particular, we perform thecalculation for parabolic $\mathrm{SL}_2(\mathbb{C})$-representation varietiesover a closed orientable surface of arbitrary genus and any number of markedpoints with holonomies of Jordan type. This technique is based on a buildingmethod of lax monoidal TQFTs of physical inspiration that generalizes theconstruction of Gonz\'alez-Prieto, Logares and Mu\~noz.

Motivic theory of representation varieties via Topological Quantum Field Theories