  We test the convergence of the QCD exponential moments by including PT
corrections to order \alpha_s^3 and the NP contributions up to D=8 <G^4>
condensates. Then, using the ratio of exponential sum rules where the QCD PT
series is more convergent, we study the correlation between the gluon
condensates <\alpha_s G^2> and < g^3f_{abc} G^3>. From charmonium systems and
using the charm quark mass as input, we deduce:< g^3f_{abc} G^3>
=(8.2+-1.0)GeV^2 <\alpha_s G^2> corresponding to < \alpha_s G^2>=(7.5+- 2.0)
10^{-2} GeV^4. Using these results for the bottomium systems, we obtain:
m_b(m_b)= 4212(32) MeV, which is slightly higher but consistent within the
errrors with the ones from Q^2-moments and their ratios: m_b(m_b)= 4172(12)
MeV. We are tempted to consider as a final result from the sum rules
approaches, the average m_b(m_b)= 4177(11) MeV of the two previous
determinations.
