The flexibility and stiffness of small DNA play a fundamental role ranging from several biophysical processes to nano-technological applications. Here, we estimate the mechanical properties of short double-stranded DNA (dsDNA) having length ranging from 12 base-pairs (bps) to 56 bps, paranemic crossover (PX) DNA, and hexagonal DNA nanotubes (DNTs) using two widely used coarse-grain models $-$ Martini and oxDNA. To calculate the persistence length ($L_p$) and the stretch modulus ($gamma$) of the dsDNA, we incorporate the worm-like chain and elastic rod model, while for DNT, we implement our previously developed theoretical framework. We compare and contrast all the results with previously reported all-atom molecular dynamics (MD) simulation and experimental results. The mechanical properties of dsDNA ($L_p$ $sim$ 50nm, $gamma sim$ 800-1500 pN), PX DNA ($gamma sim$ 1600-2000 pN) and DNTs ($L_p sim 1-10 mu$m, $gamma sim$ 6000-8000 pN) estimated using Martini soft elastic network and oxDNA are in very good agreement with the all-atom MD and experimental values, while the stiff elastic network Martini reproduces order of magnitude higher values of $L_p$ and $gamma$. The high flexibility of small dsDNA is also depicted in our calculations. However, Martini models proved inadequate to capture the salt concentration effects on the mechanical properties with increasing salt molarity. OxDNA captures the salt concentration effect on small dsDNA mechanics. But it is found to be ineffective to reproduce the salt-dependent mechanical properties of DNTs. Also, unlike Martini, the time evolved PX DNA and DNT structures from the oxDNA models are comparable to the all-atom MD simulated structures. Our findings provide a route to study the mechanical properties of DNA nanostructures with increased time and length scales and has a remarkable implication in the context of DNA nanotechnology.
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