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Is there any simpler way of proving this?

Prove that there are no integers a, b and c that satisfy the equation a3+b3=7c3+3

A, B, C and D are positive integers such that A2+3B2+3C2+5D5=1002 What is the value of A X B X C X D? Find all possible solutions.

Thanks!

F and E are midpoints of the sides AB and AC respectively in a triangle ABC. X and Y are points on the side BC such that EX and FY are parallel. Show that parallelogram EFYX has half the area of triangle ABC.