Diffusion of asymmetric diblock and triblock copolymers in a three-dimensional periodic potential field with body centered cubic (bcc) symmetry is simulated numerically using Langevin dynamics. To simulate unentangled copolymer melts, a spring and bead model (Rouse) is introduced. To simulate entangled polymer melts, a copolymer chain is only allowed to move along its contour, following a strict reptation algorithm, with fixed segment length and no contour length fluctuations. For an AB diblock copolymer with a short A block, we compute a normalized diffusion coefficient, D/D-0, where D-0 is the diffusion coefficient in the absence of potential fields. We find that D/D-0 scales according to exp(-alpha N-A) for fairly large alpha N-A regardless of the mechanism of the diffusion (Rouse or strict reptation), where alpha is the amplitude of the potential field and N-A is the number of segments in the A block. In this asymmetric regime (fraction of minority block, f = 0.1), the product alpha N-A evidently determines the diffusion of the diblock copolymer. The diffusion of ABA triblock copolymers by the Rouse mechanism also scales with alpha N-A in the same way as for diblock copolymers, where N-A for the triblock copolymer is the number of segments in each A block. That suggests that the triblock copolymer diffuses by activating only one A block at a time (walking diffusion), which is consistent with experiments. However, the strict reptation calculations show larger reduction of diffusion coefficients for triblock copolymers in the bcc potential field. Apparently, entanglements inhibit such a walking diffusion mechanism and reduce the diffusion more strongly for triblock copolymers than for diblock copolymers.