  We use supersymmetric generalised unitarity to calculate supercoefficients of
box functions in the expansion of scattering amplitudes in N=8 supergravity at
one loop. Recent advances have presented tree-level amplitudes in N=8
supergravity in terms of sums of terms containing squares of colour-ordered
Yang-Mills superamplitudes. We develop the consequences of these results for
the structure of one-loop supercoefficients, recasting them as sums of squares
of N=4 Yang-Mills expressions with certain coefficients inherited from the
tree-level superamplitudes. This provides new expressions for all one-loop box
coefficients in N=8 supergravity, which we check against known results in a
number of cases.
