  Using 180 pb^-1 of data collected with the CDF II detector at the Tevatron,
we measure the first two moments of the hadronic invariant mass-squared
distribution in charmed semileptonic B decays. From these we determine the
non-perturbative Heavy Quark Effective Theory parameters Lambda and lambda_1,
used to relate the B meson semileptonic branching ratio to the CKM matrix
element |V_cb|. For a minimum lepton momentum of 0.7 GeV/c in the B rest frame
me measure the first two moments of the D** --> D(*) pi component to be
<m^2_D**> = (5.83 +/- 0.16(stat) +/- 0.08(syst)) GeV^2, <(m^2_D** -
<m^2_D**>)^2> = (1.30 +/- 0.69(stat) +/- 0.22(syst)) GeV^4. Combining these
with the discrete mass terms from the D and D* mesons, we find the total
moments to be <M^2_Xc> - mbar_D^2 = (0.467 +/- 0.038_(stat) +/- 0.068(syst))
GeV^2, <(M^2_Xc - <M^2_Xc>)^2> = (1.05 +/- 0.26(stat) +/- 0.13(syst)) GeV^4,
where mbar_D is the spin-averaged D mass. The systematic error is dominated by
the uncertainties in the world-average branching ratios used to combine the D,
D* and D** contributions. The analysis makes no assumptions about the shape or
resonant structure of the D** --> D(*) pi invariant mass distribution.
