Let f(n)=an3+bn2+cn+d be the function that generates the given pattern where 0≤n≤4 and:
f(0)=4, f(1)=14, f(2)=76, f(4)=1364.
f(0)=4=d, so d=4;
f(1)=14=a+b+c+4,
Eqn (1): a+b+c=10
f(2)=76=8a+4b+2c+4,
Eqn (2): 8a+4b+2c=72
f(4)=1364=64a+16b+4c+4,
Eqn (3): 64a+16b+4c=1360
Eliminate c: (2)-2(1):
Eqn (4): 6a+2b=52
Eqn (5): (3)-4(1): 60a+12b=1320
Eliminate a: (5)-10(4): -8b=800, b=-100.
Substitute for b in (4): 6a-200=52, 6a=252, a=42.
Substitute for a and b in (1): 42-100+c=10, c=68.
f(n)=42n3-100n2+68n+4. f(3)=442, so series becomes 4, 14, 76, 442, 1364.
(There may be other solutions depending on the method used to solve.)